All the tests were done on an Arch Linux x86_64 machine with an Intel(R) Core(TM) i7 CPU (1.90GHz). We first load the necessary packages.
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 605.9 646.0 687.908 687.90 732.15 786.3 100
#> n1e3 1721.8 1961.1 2109.941 2078.10 2210.90 3085.6 100
#> n1e4 16073.3 18094.5 21076.900 21910.75 23083.85 29813.0 100
#> n1e5 298352.2 360827.3 417913.192 405867.85 472103.65 555172.2 100
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 1.0606 1.1127 1.154240 1.1564 1.18970 1.2833 100
#> p25 3.9486 4.0129 4.228709 4.0536 4.14350 9.5289 100
#> p100 30.8474 31.2611 36.815018 34.4899 39.31145 60.8958 100
#> p400 362.0262 391.0860 431.188940 400.9891 456.07155 657.0685 100
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.