Last updated on 2023-01-25 04:51:37 CET.
| Flavor | Version | Tinstall | Tcheck | Ttotal | Status | Flags |
|---|---|---|---|---|---|---|
| r-devel-linux-x86_64-debian-gcc | 1.0 | 15.15 | 99.10 | 114.25 | OK | |
| r-devel-linux-x86_64-fedora-clang | 1.0 | 193.20 | OK | |||
| r-devel-linux-x86_64-fedora-gcc | 1.0 | 183.45 | OK | |||
| r-release-macos-arm64 | 1.0 | 51.00 | ERROR | |||
| r-oldrel-macos-arm64 | 1.0 | 49.00 | ERROR | |||
| r-oldrel-windows-ix86+x86_64 | 1.0 | 30.00 | 145.00 | 175.00 | ERROR |
Version: 1.0
Check: PDF version of manual
Result: WARN
LaTeX errors when creating PDF version.
This typically indicates Rd problems.
LaTeX errors found:
! Undefined control sequence.
<recently read> \pmb
l.273 ...(\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.287 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.287 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.288 ...{\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.288 ...ger not less than \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.290 ...onging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.293 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.293 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.293 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},\mathcal {X}_i\right ...
l.293 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.293 }{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.304 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.304 }{}
! Misplaced alignment tab character &.
<recently read> &
l.304 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.304 }{}
! LaTeX Error: \begin{list} on input line 266 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.305 ...he integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.314 ...code{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.314 ... (i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.315 ...d}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
in the reduced model when...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.319 ...size for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.323 ...w}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
for each value of the se...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.324 ...}] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.329 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.506 ...(\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.520 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.520 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.521 ...{\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.521 ...ger not less than \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.523 ...onging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.526 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.526 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.526 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},\mathcal {X}_i\right ...
l.526 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.526 }{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.537 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.537 }{}
! Misplaced alignment tab character &.
<recently read> &
l.537 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.537 }{}
! LaTeX Error: \begin{list} on input line 499 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.538 ...he integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.547 ...code{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.547 ... (i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.548 ...d}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
in the reduced model when...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.552 ...size for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.556 ...w}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.557 ...}] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.562 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> h\in \mathbb
{R}^+
l.740 \item{} \eqn{h\in \mathbb{R}^+}{}
is the bandwidth.
! Undefined control sequence.
<argument> k\in \mathbb
{Z}^+
l.1013 \item{} \eqn{k\in \mathbb{Z}^+}{}
is a smoothing factor (the number o...
! Undefined control sequence.
<argument> ...\hat {\theta }}=\min \{h\in \mathbb
{R}^+ \text { such that } ...
l.1019 ...}^n1_{B_{\hat{\theta}}(x,h)}(X_i)=k\}}{}
, where \eqn{1_{B_{\hat{\t...
! Undefined control sequence.
<argument> ... }}=\min \{h\in \mathbb {R}^+ \text
{ such that } \sum _{i=1}^...
l.1019 ...}^n1_{B_{\hat{\theta}}(x,h)}(X_i)=k\}}{}
, where \eqn{1_{B_{\hat{\t...
! Undefined control sequence.
<argument> ...,\theta }=\min \left \{h\in \mathbb
{R}^+ \text { such that } ...
l.1158 ...}^n1_{B_{\theta}(x,h)}(X_i)=k\right\}}{}
, where \eqn{1_{B_{\theta}...
! Undefined control sequence.
<argument> ...in \left \{h\in \mathbb {R}^+ \text
{ such that } \sum _{i=1}^...
l.1158 ...}^n1_{B_{\theta}(x,h)}(X_i)=k\right\}}{}
, where \eqn{1_{B_{\theta}...
! Undefined control sequence.
<recently read> \pmb
l.1340 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1350 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1353 }{}
! Undefined control sequence.
<recently read> \pmb
l.1355 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.1355 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.1355 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.1355 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.1360 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
(see the documentation of...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.1366 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.1366 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.1367 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1367 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1369 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.1372 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.1372 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.1372 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},X_i\right >\right )+\...
l.1372 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.1372 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.1378 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.1384 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.1384 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.1385 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1385 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.1388 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.1388 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.1388 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1389 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.1391 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+r^{\pmb {2}}\left (\...
l.1391 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+r^{\pmb
{2}}\left (\left <\theta _...
l.1391 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...b {2}}\left (\left <\theta _0^{\pmb
{2}},X_i\right >\right )+\...
l.1391 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{2}}.
l.1391 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.1408 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.1408 }{}
! Misplaced alignment tab character &.
<recently read> &
l.1408 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.1408 }{}
! LaTeX Error: \begin{list} on input line 1333 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1409 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.1418 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.1418 ...(i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1422 ...ize for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<recently read> \pmb
l.1426 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.1426 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{2}}
l.1427 ...] Estimate of \eqn{\theta_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1432 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.1433 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.1433 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.1434 ...] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1438 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.1618 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1628 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1631 }{}
! Undefined control sequence.
<recently read> \pmb
l.1633 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.1633 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.1633 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.1633 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.1638 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
(see the documentation of...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.1644 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.1644 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.1645 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1645 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1647 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.1650 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.1650 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.1650 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},X_i\right >\right )+\...
l.1650 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.1650 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.1656 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.1662 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.1662 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.1663 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1663 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.1666 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.1666 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.1666 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1667 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.1669 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+r^{\pmb {2}}\left (\...
l.1669 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+r^{\pmb
{2}}\left (\left <\theta _...
l.1669 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...b {2}}\left (\left <\theta _0^{\pmb
{2}},X_i\right >\right )+\...
l.1669 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{2}}.
l.1669 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.1686 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.1686 }{}
! Misplaced alignment tab character &.
<recently read> &
l.1686 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.1686 }{}
! LaTeX Error: \begin{list} on input line 1611 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1687 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.1698 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i.e. estimate of \eqn{\p...
! Undefined control sequence.
<recently read> \pmb
l.1698 ... (i.e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<recently read> \pmb
l.1706 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.1706 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{2}}
l.1707 ...] Estimate of \eqn{\theta_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1712 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.1713 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.1713 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.1714 ...] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1718 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \mathbb
l.1854 ...ates taking values in \eqn{\mathbb{R}}{}
. In this equation, \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.1854 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.1854 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta }\right )=\frac {1}{2}\left (\pmb...
l.1859 }{}
! Undefined control sequence.
<argument> ...a }\right )=\frac {1}{2}\left (\pmb
{Y}-\pmb {Z}\pmb {\beta }\...
l.1859 }{}
! Undefined control sequence.
<argument> ... )=\frac {1}{2}\left (\pmb {Y}-\pmb
{Z}\pmb {\beta }\right )^{...
l.1859 }{}
! Undefined control sequence.
<argument> ... {1}{2}\left (\pmb {Y}-\pmb {Z}\pmb
{\beta }\right )^{\top }\l...
l.1859 }{}
! Undefined control sequence.
<argument> ...{\beta }\right )^{\top }\left (\pmb
{Y}-\pmb {Z}\pmb {\beta }\...
l.1859 }{}
! Undefined control sequence.
<argument> ...right )^{\top }\left (\pmb {Y}-\pmb
{Z}\pmb {\beta }\right )+n...
l.1859 }{}
! Undefined control sequence.
<argument> ...{\top }\left (\pmb {Y}-\pmb {Z}\pmb
{\beta }\right )+n\sum _{j...
l.1859 }{}
! Undefined control sequence.
<recently read> \pmb
l.1861 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.3356 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3366 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3369 }{}
! Undefined control sequence.
<recently read> \pmb
l.3371 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.3371 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.3371 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.3371 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.3376 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.3382 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.3382 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.3383 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3383 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3385 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.3388 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+\varepsilon _i^{\pmb...
l.3388 }{}
! Undefined control sequence.
<argument> ..._k^{\pmb {1}})+\varepsilon _i^{\pmb
{1}}.
l.3388 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.3394 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.3400 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.3400 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.3401 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3401 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.3404 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.3404 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.3404 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3405 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.3407 ...k^{\pmb{2}})+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+\varepsilon _i^{\pmb...
l.3407 ...k^{\pmb{2}})+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ..._k^{\pmb {2}})+\varepsilon _i^{\pmb
{2}}.
l.3407 ...k^{\pmb{2}})+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.3424 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.3424 }{}
! Misplaced alignment tab character &.
<recently read> &
l.3424 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.3424 }{}
! LaTeX Error: \begin{list} on input line 3349 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3425 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.3434 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.3434 ...(i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3436 ...ize for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<recently read> \pmb
l.3439 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.3439 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3443 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3444 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.3444 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3447 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3609 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3619 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3622 }{}
! Undefined control sequence.
<recently read> \pmb
l.3624 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.3624 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.3624 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.3624 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.3629 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.3635 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.3635 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.3636 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3636 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3638 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.3641 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+m^{\pmb {1}}\left (X...
l.3641 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+m^{\pmb
{1}}\left (X_i\right )+\va...
l.3641 }{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{1}}.
l.3641 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.3647 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.3653 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.3653 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.3654 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3654 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.3657 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.3657 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.3657 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3658 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.3660 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+m^{\pmb {2}}\left (X...
l.3660 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+m^{\pmb
{2}}\left (X_i\right )+\va...
l.3660 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{2}}.
l.3660 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.3677 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.3677 }{}
! Misplaced alignment tab character &.
<recently read> &
l.3677 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.3677 }{}
! LaTeX Error: \begin{list} on input line 3602 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3678 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.3687 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.3687 ...(i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3690 ...ize for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<recently read> \pmb
l.3694 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.3694 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3699 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3700 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.3700 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3704 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3877 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3887 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3890 }{}
! Undefined control sequence.
<recently read> \pmb
l.3892 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.3892 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.3892 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.3892 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.3897 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.3903 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.3903 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.3904 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3904 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3906 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.3909 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+m^{\pmb {1}}\left (X...
l.3909 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+m^{\pmb
{1}}\left (X_i\right )+\va...
l.3909 }{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{1}}.
l.3909 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.3915 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.3921 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.3921 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.3922 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3922 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.3925 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.3925 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.3925 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3926 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.3928 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+m^{\pmb {2}}\left (X...
l.3928 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+m^{\pmb
{2}}\left (X_i\right )+\va...
l.3928 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{2}}.
l.3928 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.3945 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.3945 }{}
! Misplaced alignment tab character &.
<recently read> &
l.3945 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.3945 }{}
! LaTeX Error: \begin{list} on input line 3870 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3946 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.3955 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i.e. estimate of \eqn{\p...
! Undefined control sequence.
<recently read> \pmb
l.3955 ... (i.e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<recently read> \pmb
l.3962 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.3962 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3967 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3968 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.3968 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3972 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \mathbb
l.4219 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4220 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4220 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}\approx \widetilde {\pmb {Z}}\pmb {\beta }_0...
l.4226 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ... {\pmb {Y}}\approx \widetilde {\pmb
{Z}}\pmb {\beta }_0+\pmb {...
l.4226 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...}}\approx \widetilde {\pmb {Z}}\pmb
{\beta }_0+\pmb {\varepsil...
l.4226 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...ilde {\pmb {Z}}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4226 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta }\right )=\frac {1}{2}\left (\wid...
l.4230 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4230 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )^...
l.4230 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )^{\top }\l...
l.4230 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4230 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )+...
l.4230 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )+n\sum _{j...
l.4230 }{}
! Undefined control sequence.
<recently read> \pmb
l.4232 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4236 ..., after estimating \eqn{\pmb{\beta}_0}{}
by minimising (1), we dea...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4237 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4237 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<recently read> \mathbb
l.4412 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4413 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4413 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}\approx \widetilde {\pmb {Z}}\pmb {\beta }_0...
l.4419 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ... {\pmb {Y}}\approx \widetilde {\pmb
{Z}}\pmb {\beta }_0+\pmb {...
l.4419 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...}}\approx \widetilde {\pmb {Z}}\pmb
{\beta }_0+\pmb {\varepsil...
l.4419 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...ilde {\pmb {Z}}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4419 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta }\right )=\frac {1}{2}\left (\wid...
l.4423 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4423 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )^...
l.4423 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )^{\top }\l...
l.4423 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4423 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )+...
l.4423 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )+n\sum _{j...
l.4423 }{}
! Undefined control sequence.
<recently read> \pmb
l.4425 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4429 ..., after estimating \eqn{\pmb{\beta}_0}{}
by minimising (1), we dea...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4430 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4430 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<recently read> \mathbb
l.4609 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4610 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4610 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}_{\theta _0}\approx \widetilde {\pmb {Z}}_{\...
l.4616 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...{\theta _0}\approx \widetilde {\pmb
{Z}}_{\theta _0}\pmb {\bet...
l.4616 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...idetilde {\pmb {Z}}_{\theta _0}\pmb
{\beta }_0+\pmb {\varepsil...
l.4616 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...Z}}_{\theta _0}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4616 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> (\pmb
{\beta },\theta )
l.4617 ...er the pair \eqn{(\pmb{\beta},\theta)}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta },\theta \right )=\frac {1}{2}\le...
l.4620 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4620 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4620 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )^{\top }\l...
l.4620 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4620 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4620 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )+n\sum _{j...
l.4620 }{}
! Undefined control sequence.
<recently read> \pmb
l.4622 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4629 ..., after estimating \eqn{\pmb{\beta}_0}{}
and \eqn{\theta_0}{} by m...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4630 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4630 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<recently read> \mathbb
l.4838 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4839 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4839 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}_{\theta _0}\approx \widetilde {\pmb {Z}}_{\...
l.4845 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...{\theta _0}\approx \widetilde {\pmb
{Z}}_{\theta _0}\pmb {\bet...
l.4845 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...idetilde {\pmb {Z}}_{\theta _0}\pmb
{\beta }_0+\pmb {\varepsil...
l.4845 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...Z}}_{\theta _0}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4845 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> (\pmb
{\beta },\theta )
l.4846 ...er the pair \eqn{(\pmb{\beta},\theta)}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta },\theta \right )=\frac {1}{2}\le...
l.4849 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4849 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4849 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )^{\top }\l...
l.4849 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4849 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4849 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )+n\sum _{j...
l.4849 }{}
! Undefined control sequence.
<recently read> \pmb
l.4851 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4857 ..., after estimating \eqn{\pmb{\beta}_0}{}
and \eqn{\theta_0}{} by m...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4858 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4858 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.4872 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. the estimate of \e...
! Undefined control sequence.
<recently read> \pmb
l.4872 ...e. the estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<recently read> \pmb
l.4878 ...n used to estimate \eqn{\pmb{\beta}_0}{}
and \eqn{\theta_0}{}. Tha...
! Undefined control sequence.
<recently read> \pmb
l.4884 used by the optimal \eqn{\pmb{\beta}}{}
for each \eqn{\theta}{} in \e...
Flavor: r-release-macos-arm64
Version: 1.0
Check: PDF version of manual without index
Result: ERROR
Flavor: r-release-macos-arm64
Version: 1.0
Check: PDF version of manual
Result: WARN
LaTeX errors when creating PDF version.
This typically indicates Rd problems.
LaTeX errors found:
! Undefined control sequence.
<recently read> \pmb
l.271 ...(\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.285 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.285 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.286 ...{\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.286 ...ger not less than \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.288 ...onging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.291 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.291 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.291 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},\mathcal {X}_i\right ...
l.291 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.291 }{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.302 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.302 }{}
! Misplaced alignment tab character &.
<recently read> &
l.302 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.302 }{}
! LaTeX Error: \begin{list} on input line 264 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.303 ...he integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.312 ...code{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.312 ... (i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.313 ...d}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
in the reduced model when...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.317 ...size for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.321 ...w}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
for each value of the se...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.322 ...}] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.327 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.504 ...(\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.518 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.518 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.519 ...{\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.519 ...ger not less than \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.521 ...onging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.524 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.524 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.524 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},\mathcal {X}_i\right ...
l.524 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.524 }{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.535 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.535 }{}
! Misplaced alignment tab character &.
<recently read> &
l.535 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.535 }{}
! LaTeX Error: \begin{list} on input line 497 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.536 ...he integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.545 ...code{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.545 ... (i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.546 ...d}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
in the reduced model when...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.550 ...size for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<argument> \beta _0^{\pmb
{1}}
l.554 ...w}] Estimate of \eqn{\beta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.555 ...}] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.560 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> h\in \mathbb
{R}^+
l.738 \item{} \eqn{h\in \mathbb{R}^+}{}
is the bandwidth.
! Undefined control sequence.
<argument> k\in \mathbb
{Z}^+
l.1011 \item{} \eqn{k\in \mathbb{Z}^+}{}
is a smoothing factor (the number o...
! Undefined control sequence.
<argument> ...\hat {\theta }}=\min \{h\in \mathbb
{R}^+ \text { such that } ...
l.1017 ...}^n1_{B_{\hat{\theta}}(x,h)}(X_i)=k\}}{}
, where \eqn{1_{B_{\hat{\t...
! Undefined control sequence.
<argument> ... }}=\min \{h\in \mathbb {R}^+ \text
{ such that } \sum _{i=1}^...
l.1017 ...}^n1_{B_{\hat{\theta}}(x,h)}(X_i)=k\}}{}
, where \eqn{1_{B_{\hat{\t...
! Undefined control sequence.
<argument> ...,\theta }=\min \left \{h\in \mathbb
{R}^+ \text { such that } ...
l.1156 ...}^n1_{B_{\theta}(x,h)}(X_i)=k\right\}}{}
, where \eqn{1_{B_{\theta}...
! Undefined control sequence.
<argument> ...in \left \{h\in \mathbb {R}^+ \text
{ such that } \sum _{i=1}^...
l.1156 ...}^n1_{B_{\theta}(x,h)}(X_i)=k\right\}}{}
, where \eqn{1_{B_{\theta}...
! Undefined control sequence.
<recently read> \pmb
l.1338 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1348 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1351 }{}
! Undefined control sequence.
<recently read> \pmb
l.1353 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.1353 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.1353 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.1353 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.1358 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
(see the documentation of...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.1364 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.1364 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.1365 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1365 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1367 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.1370 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.1370 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.1370 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},X_i\right >\right )+\...
l.1370 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.1370 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.1376 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.1382 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.1382 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.1383 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1383 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.1386 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.1386 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.1386 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1387 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.1389 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+r^{\pmb {2}}\left (\...
l.1389 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+r^{\pmb
{2}}\left (\left <\theta _...
l.1389 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...b {2}}\left (\left <\theta _0^{\pmb
{2}},X_i\right >\right )+\...
l.1389 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{2}}.
l.1389 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.1406 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.1406 }{}
! Misplaced alignment tab character &.
<recently read> &
l.1406 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.1406 }{}
! LaTeX Error: \begin{list} on input line 1331 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1407 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.1416 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.1416 ...(i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1420 ...ize for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<recently read> \pmb
l.1424 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.1424 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{2}}
l.1425 ...] Estimate of \eqn{\theta_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1430 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.1431 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.1431 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.1432 ...] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1436 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.1616 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1626 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.1629 }{}
! Undefined control sequence.
<recently read> \pmb
l.1631 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.1631 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.1631 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.1631 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.1636 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
(see the documentation of...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.1642 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.1642 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.1643 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1643 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1645 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.1648 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+r^{\pmb {1}}\left (\...
l.1648 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+r^{\pmb
{1}}\left (\left <\theta _...
l.1648 }{}
! Undefined control sequence.
<argument> ...b {1}}\left (\left <\theta _0^{\pmb
{1}},X_i\right >\right )+\...
l.1648 }{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{1}}.
l.1648 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.1654 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.1660 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.1660 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.1661 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1661 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.1664 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.1664 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.1664 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1665 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.1667 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+r^{\pmb {2}}\left (\...
l.1667 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+r^{\pmb
{2}}\left (\left <\theta _...
l.1667 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...b {2}}\left (\left <\theta _0^{\pmb
{2}},X_i\right >\right )+\...
l.1667 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...ight >\right )+\varepsilon _i^{\pmb
{2}}.
l.1667 ...ight>\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.1684 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.1684 }{}
! Misplaced alignment tab character &.
<recently read> &
l.1684 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.1684 }{}
! LaTeX Error: \begin{list} on input line 1609 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.1685 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.1696 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i.e. estimate of \eqn{\p...
! Undefined control sequence.
<recently read> \pmb
l.1696 ... (i.e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<recently read> \pmb
l.1704 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.1704 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{2}}
l.1705 ...] Estimate of \eqn{\theta_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.1710 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.1711 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.1711 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \theta _0^{\pmb
{1}}
l.1712 ...] Estimate of \eqn{\theta_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.1716 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \mathbb
l.1852 ...ates taking values in \eqn{\mathbb{R}}{}
. In this equation, \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.1852 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.1852 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta }\right )=\frac {1}{2}\left (\pmb...
l.1857 }{}
! Undefined control sequence.
<argument> ...a }\right )=\frac {1}{2}\left (\pmb
{Y}-\pmb {Z}\pmb {\beta }\...
l.1857 }{}
! Undefined control sequence.
<argument> ... )=\frac {1}{2}\left (\pmb {Y}-\pmb
{Z}\pmb {\beta }\right )^{...
l.1857 }{}
! Undefined control sequence.
<argument> ... {1}{2}\left (\pmb {Y}-\pmb {Z}\pmb
{\beta }\right )^{\top }\l...
l.1857 }{}
! Undefined control sequence.
<argument> ...{\beta }\right )^{\top }\left (\pmb
{Y}-\pmb {Z}\pmb {\beta }\...
l.1857 }{}
! Undefined control sequence.
<argument> ...right )^{\top }\left (\pmb {Y}-\pmb
{Z}\pmb {\beta }\right )+n...
l.1857 }{}
! Undefined control sequence.
<argument> ...{\top }\left (\pmb {Y}-\pmb {Z}\pmb
{\beta }\right )+n\sum _{j...
l.1857 }{}
! Undefined control sequence.
<recently read> \pmb
l.1859 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.3354 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3364 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3367 }{}
! Undefined control sequence.
<recently read> \pmb
l.3369 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.3369 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.3369 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.3369 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.3374 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.3380 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.3380 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.3381 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3381 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3383 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.3386 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+\varepsilon _i^{\pmb...
l.3386 }{}
! Undefined control sequence.
<argument> ..._k^{\pmb {1}})+\varepsilon _i^{\pmb
{1}}.
l.3386 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.3392 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.3398 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.3398 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.3399 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3399 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.3402 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.3402 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.3402 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3403 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.3405 ...k^{\pmb{2}})+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+\varepsilon _i^{\pmb...
l.3405 ...k^{\pmb{2}})+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ..._k^{\pmb {2}})+\varepsilon _i^{\pmb
{2}}.
l.3405 ...k^{\pmb{2}})+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.3422 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.3422 }{}
! Misplaced alignment tab character &.
<recently read> &
l.3422 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.3422 }{}
! LaTeX Error: \begin{list} on input line 3347 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3423 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.3432 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.3432 ...(i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3434 ...ize for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<recently read> \pmb
l.3437 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.3437 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3441 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3442 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.3442 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3445 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3607 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3617 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3620 }{}
! Undefined control sequence.
<recently read> \pmb
l.3622 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.3622 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.3622 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.3622 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.3627 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.3633 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.3633 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.3634 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3634 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3636 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.3639 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+m^{\pmb {1}}\left (X...
l.3639 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+m^{\pmb
{1}}\left (X_i\right )+\va...
l.3639 }{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{1}}.
l.3639 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.3645 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.3651 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.3651 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.3652 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3652 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.3655 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.3655 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.3655 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3656 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.3658 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+m^{\pmb {2}}\left (X...
l.3658 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+m^{\pmb
{2}}\left (X_i\right )+\va...
l.3658 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{2}}.
l.3658 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.3675 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.3675 }{}
! Misplaced alignment tab character &.
<recently read> &
l.3675 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.3675 }{}
! LaTeX Error: \begin{list} on input line 3600 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3676 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.3685 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. estimate of \eqn{\...
! Undefined control sequence.
<recently read> \pmb
l.3685 ...(i. e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3688 ...ize for \eqn{\mathcal{R}_n^{\pmb{1}}}{}
.
! Undefined control sequence.
<recently read> \pmb
l.3692 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.3692 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3697 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3698 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.3698 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3702 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3875 ...\beta_{01},\dots,\beta_{0p_n})^{\top}}{}
is a vector of unknown re...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3885 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}=\{(\zeta _i,\mathcal {X}_i,Y_i),\quad i=...
l.3888 }{}
! Undefined control sequence.
<recently read> \pmb
l.3890 The superscript \eqn{\pmb{s}}{}
with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{} ...
! Undefined control sequence.
<recently read> \pmb
l.3890 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb
{1},\pmb {2}
l.3890 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \pmb {s}=\pmb {1},\pmb
{2}
l.3890 ...}{} with \eqn{\pmb{s}=\pmb{1},\pmb{2}}{}
indicates the stage of th...
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{1}}
l.3895 ... subsample \eqn{\mathcal{E}^{\pmb{1}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}=\left \{\zeta \left (t_k^{\pmb {1}}\ri...
l.3901 }{}
! Undefined control sequence.
<argument> ...{1}}=\left \{\zeta \left (t_k^{\pmb
{1}}\right ),\ \ k=1,\dots...
l.3901 }{}
! Undefined control sequence.
<argument> t_k^{\pmb
{1}}=t_{\left [(2k-1)q_n/2\right ]}
l.3902 ...\pmb{1}}=t_{\left[(2k-1)q_n/2\right]}}{}
and \eqn{\left[z\right]}...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3902 ...er not less than \eqn{z\in\mathbb{R}}{}
.The size (cardinal) of th...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3904 ...nging to \eqn{\mathcal{R}_n^{\pmb{1}}}{}
:
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{w_n}\beta _{0k}^{\pmb
{1}}\zeta _i(t_k^{\pmb {1}...
l.3907 }{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {1}}\zeta _i(t_k^{\pmb
{1}})+m^{\pmb {1}}\left (X...
l.3907 }{}
! Undefined control sequence.
<argument> ...1}}\zeta _i(t_k^{\pmb {1}})+m^{\pmb
{1}}\left (X_i\right )+\va...
l.3907 }{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{1}}.
l.3907 }{}
! Undefined control sequence.
<argument> \mathcal {E}^{\pmb
{2}}
l.3913 ... subsample \eqn{\mathcal{E}^{\pmb{2}}}{}
. Specifically:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\bigcup _{\left \{k,\widehat {\beta }_...
l.3919 }{}
! Undefined control sequence.
<argument> ...ft \{k,\widehat {\beta }_{0k}^{\pmb
{1}}\not =0\right \}}\left...
l.3919 }{}
! Undefined control sequence.
<argument> r_n=\sharp (\mathcal {R}_n^{\pmb
{2}})
l.3920 ...n{r_n=\sharp(\mathcal{R}_n^{\pmb{2}})}{}
, we can rename the variab...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3920 ...ables in \eqn{\mathcal{R}_n^{\pmb{2}}}{}
as follows:
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}=\left \{\zeta (t_1^{\pmb {2}}),\dots ,...
l.3923 }{}
! Undefined control sequence.
<argument> ...{\pmb {2}}=\left \{\zeta (t_1^{\pmb
{2}}),\dots ,\zeta (t_{r_n...
l.3923 }{}
! Undefined control sequence.
<argument> ...b {2}}),\dots ,\zeta (t_{r_n}^{\pmb
{2}})\right \},
l.3923 }{}
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3924 ...nging to \eqn{\mathcal{R}_n^{\pmb{2}}}{}
! Undefined control sequence.
<argument> ...=\sum _{k=1}^{r_n}\beta _{0k}^{\pmb
{2}}\zeta _i(t_k^{\pmb {2}...
l.3926 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ... _{0k}^{\pmb {2}}\zeta _i(t_k^{\pmb
{2}})+m^{\pmb {2}}\left (X...
l.3926 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...2}}\zeta _i(t_k^{\pmb {2}})+m^{\pmb
{2}}\left (X_i\right )+\va...
l.3926 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! Undefined control sequence.
<argument> ...t (X_i\right )+\varepsilon _i^{\pmb
{2}}.
l.3926 ...t(X_i\right)+\varepsilon_i^{\pmb{2}}.}{}
! LaTeX Error: Environment aligned undefined.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Misplaced alignment tab character &.
<argument> q_{n,k}= \left \{\begin {aligned} &
[p_n/w_n]+1& \quad k\in \{1,\...
l.3943 }{}
! Misplaced alignment tab character &.
<argument> ...eft \{\begin {aligned} &[p_n/w_n]+1&
\quad k\in \{1,\dots ,p_n...
l.3943 }{}
! Misplaced alignment tab character &.
<recently read> &
l.3943 }{}
! Misplaced alignment tab character &.
<argument> ...s ,p_n-w_n[p_n/w_n]\},\\ &[p_n/w_n]&
\quad k\in \{p_n-w_n[p_n/w...
l.3943 }{}
! LaTeX Error: \begin{list} on input line 3868 ended by \end{aligned}.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
! Undefined control sequence.
<argument> z\in \mathbb
{R}
l.3944 ...e integer part of \eqn{z\in\mathbb{R}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.3953 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i.e. estimate of \eqn{\p...
! Undefined control sequence.
<recently read> \pmb
l.3953 ... (i.e. estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<recently read> \pmb
l.3960 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{2}}
l.3960 ...imate of \eqn{\pmb{\beta}_0^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{2}}
l.3965 ...to build \eqn{\mathcal{R}_n^{\pmb{2}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \pmb
l.3966 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \pmb {\beta }_0^{\pmb
{1}}
l.3966 ...imate of \eqn{\pmb{\beta}_0^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<argument> \mathcal {R}_n^{\pmb
{1}}
l.3970 ...to build \eqn{\mathcal{R}_n^{\pmb{1}}}{}
for each value of the seq...
! Undefined control sequence.
<recently read> \mathbb
l.4217 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4218 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4218 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}\approx \widetilde {\pmb {Z}}\pmb {\beta }_0...
l.4224 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ... {\pmb {Y}}\approx \widetilde {\pmb
{Z}}\pmb {\beta }_0+\pmb {...
l.4224 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...}}\approx \widetilde {\pmb {Z}}\pmb
{\beta }_0+\pmb {\varepsil...
l.4224 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...ilde {\pmb {Z}}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4224 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta }\right )=\frac {1}{2}\left (\wid...
l.4228 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4228 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )^...
l.4228 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )^{\top }\l...
l.4228 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4228 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )+...
l.4228 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )+n\sum _{j...
l.4228 }{}
! Undefined control sequence.
<recently read> \pmb
l.4230 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4234 ..., after estimating \eqn{\pmb{\beta}_0}{}
by minimising (1), we dea...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4235 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4235 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<recently read> \mathbb
l.4410 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4411 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4411 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
and \eqn{m(\cdot)}{} are ...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}\approx \widetilde {\pmb {Z}}\pmb {\beta }_0...
l.4417 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ... {\pmb {Y}}\approx \widetilde {\pmb
{Z}}\pmb {\beta }_0+\pmb {...
l.4417 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...}}\approx \widetilde {\pmb {Z}}\pmb
{\beta }_0+\pmb {\varepsil...
l.4417 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...ilde {\pmb {Z}}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4417 ...b{Z}}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta }\right )=\frac {1}{2}\left (\wid...
l.4421 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4421 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )^...
l.4421 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )^{\top }\l...
l.4421 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}-\widetilde {\pmb {Z}}...
l.4421 }{}
! Undefined control sequence.
<argument> ...detilde {\pmb {Y}}-\widetilde {\pmb
{Z}}\pmb {\beta }\right )+...
l.4421 }{}
! Undefined control sequence.
<argument> ...\pmb {Y}}-\widetilde {\pmb {Z}}\pmb
{\beta }\right )+n\sum _{j...
l.4421 }{}
! Undefined control sequence.
<recently read> \pmb
l.4423 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4427 ..., after estimating \eqn{\pmb{\beta}_0}{}
by minimising (1), we dea...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4428 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4428 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<recently read> \mathbb
l.4607 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4608 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4608 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}_{\theta _0}\approx \widetilde {\pmb {Z}}_{\...
l.4614 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...{\theta _0}\approx \widetilde {\pmb
{Z}}_{\theta _0}\pmb {\bet...
l.4614 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...idetilde {\pmb {Z}}_{\theta _0}\pmb
{\beta }_0+\pmb {\varepsil...
l.4614 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...Z}}_{\theta _0}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4614 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> (\pmb
{\beta },\theta )
l.4615 ...er the pair \eqn{(\pmb{\beta},\theta)}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta },\theta \right )=\frac {1}{2}\le...
l.4618 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4618 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4618 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )^{\top }\l...
l.4618 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4618 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4618 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )+n\sum _{j...
l.4618 }{}
! Undefined control sequence.
<recently read> \pmb
l.4620 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4627 ..., after estimating \eqn{\pmb{\beta}_0}{}
and \eqn{\theta_0}{} by m...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4628 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4628 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<recently read> \mathbb
l.4836 ...ates taking values in \eqn{\mathbb{R}}{}
and \eqn{X_i}{} is a func...
! Undefined control sequence.
<recently read> \pmb
l.4837 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> ...,\beta _{0p_n})^{\top } \in \mathbb
{R}^{p_n}
l.4837 ...a_{0p_n})^{\top} \in \mathbb{R}^{p_n}}{}
, \eqn{\theta_0\in\mathcal...
! Undefined control sequence.
<argument> \widetilde {\pmb
{Y}}_{\theta _0}\approx \widetilde {\pmb {Z}}_{\...
l.4843 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...{\theta _0}\approx \widetilde {\pmb
{Z}}_{\theta _0}\pmb {\bet...
l.4843 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...idetilde {\pmb {Z}}_{\theta _0}\pmb
{\beta }_0+\pmb {\varepsil...
l.4843 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> ...Z}}_{\theta _0}\pmb {\beta }_0+\pmb
{\varepsilon },
l.4843 ...ta_0}\pmb{\beta}_0+\pmb{\varepsilon},}{}
! Undefined control sequence.
<argument> (\pmb
{\beta },\theta )
l.4844 ...er the pair \eqn{(\pmb{\beta},\theta)}{}
! Undefined control sequence.
<argument> \mathcal {Q}\left (\pmb
{\beta },\theta \right )=\frac {1}{2}\le...
l.4847 }{}
! Undefined control sequence.
<argument> ...\frac {1}{2}\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4847 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4847 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )^{\top }\l...
l.4847 }{}
! Undefined control sequence.
<argument> ...ht )^{\top }\left (\widetilde {\pmb
{Y}}_{\theta }-\widetilde ...
l.4847 }{}
! Undefined control sequence.
<argument> ...pmb {Y}}_{\theta }-\widetilde {\pmb
{Z}}_{\theta }\pmb {\beta ...
l.4847 }{}
! Undefined control sequence.
<argument> ...\widetilde {\pmb {Z}}_{\theta }\pmb
{\beta }\right )+n\sum _{j...
l.4847 }{}
! Undefined control sequence.
<recently read> \pmb
l.4849 ...{P}_{\lambda_{j_n}}\left(\cdot\right)}{}
is a penalty function (sp...
! Undefined control sequence.
<recently read> \pmb
l.4855 ..., after estimating \eqn{\pmb{\beta}_0}{}
and \eqn{\theta_0}{} by m...
! Undefined control sequence.
<argument> Y_i-\pmb
{Z}_i^{\top }\widehat {\pmb {\beta }}
l.4856 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> Y_i-\pmb {Z}_i^{\top }\widehat {\pmb
{\beta }}
l.4856 ...\pmb{Z}_i^{\top}\widehat{\pmb{\beta}}}{}
.
! Undefined control sequence.
<argument> \hat {\pmb
{\beta }}
l.4870 ...ode{beta.est}] \eqn{\hat{\pmb{\beta}}}{}
(i. e. the estimate of \e...
! Undefined control sequence.
<recently read> \pmb
l.4870 ...e. the estimate of \eqn{\pmb{\beta}_0}{}
when the optimal tuning p...
! Undefined control sequence.
<recently read> \pmb
l.4876 ...n used to estimate \eqn{\pmb{\beta}_0}{}
and \eqn{\theta_0}{}. Tha...
! Undefined control sequence.
<recently read> \pmb
l.4882 used by the optimal \eqn{\pmb{\beta}}{}
for each \eqn{\theta}{} in \e...
Flavors: r-oldrel-macos-arm64, r-oldrel-windows-ix86+x86_64
Version: 1.0
Check: PDF version of manual without hyperrefs or index
Result: ERROR
Flavors: r-oldrel-macos-arm64, r-oldrel-windows-ix86+x86_64