Empirical likelihood computation
We show the performance of computing empirical likelihood with
el_mean(). We test the computation speed with simulated
data sets in two different settings: 1) the number of observations
increases with the number of parameters fixed, and 2) the number of
parameters increases with the number of observations fixed.
Increasing the number of observations
We fix the number of parameters at \(p =
10\), and simulate the parameter value and \(n \times p\) matrices using
rnorm(). In order to ensure convergence with a large \(n\), we set a large threshold value using
el_control().
set.seed(3175775)
p <- 10
par <- rnorm(p, sd = 0.1)
ctrl <- el_control(th = 1e+10)
result <- microbenchmark(
n1e2 = el_mean(matrix(rnorm(100 * p), ncol = p), par = par, control = ctrl),
n1e3 = el_mean(matrix(rnorm(1000 * p), ncol = p), par = par, control = ctrl),
n1e4 = el_mean(matrix(rnorm(10000 * p), ncol = p), par = par, control = ctrl),
n1e5 = el_mean(matrix(rnorm(100000 * p), ncol = p), par = par, control = ctrl)
)Below are the results:
result
#> Unit: microseconds
#> expr min lq mean median uq max neval
#> n1e2 739.344 788.7035 825.313 816.979 851.8345 1280.260 100
#> n1e3 2076.968 2334.9270 2544.438 2493.985 2693.3650 3344.997 100
#> n1e4 19767.768 23754.4475 26536.068 27109.935 28998.7000 37116.624 100
#> n1e5 338185.628 397765.4175 463856.934 446782.174 527553.9385 710010.555 100
#> cld
#> a
#> a
#> b
#> c
autoplot(result)
Increasing the number of parameters
This time we fix the number of observations at \(n = 1000\), and evaluate empirical likelihood at zero vectors of different sizes.
n <- 1000
result2 <- microbenchmark(
p5 = el_mean(matrix(rnorm(n * 5), ncol = 5),
par = rep(0, 5),
control = ctrl
),
p25 = el_mean(matrix(rnorm(n * 25), ncol = 25),
par = rep(0, 25),
control = ctrl
),
p100 = el_mean(matrix(rnorm(n * 100), ncol = 100),
par = rep(0, 100),
control = ctrl
),
p400 = el_mean(matrix(rnorm(n * 400), ncol = 400),
par = rep(0, 400),
control = ctrl
)
)result2
#> Unit: milliseconds
#> expr min lq mean median uq max neval
#> p5 1.235930 1.276739 1.361866 1.324769 1.381810 2.680283 100
#> p25 4.830289 4.878286 5.015790 4.933391 4.970878 8.417014 100
#> p100 39.227604 43.593835 47.621764 44.439667 52.253316 81.381684 100
#> p400 445.862598 491.519903 555.848706 530.848306 611.759095 783.564377 100
#> cld
#> a
#> a
#> b
#> c
autoplot(result2)
On average, evaluating empirical likelihood with a 100000×10 or 1000×400
matrix at a parameter value satisfying the convex hull constraint takes
less than a second.