All the tests were done on an Arch Linux x86_64 machine with an Intel(R) Core(TM) i7 CPU (1.90GHz).
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.
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()
.
library(ggplot2)
library(microbenchmark)
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
#> n1e2 503.713 609.8135 771.2386 658.3025 726.140 4645.336
#> n1e3 1324.759 1679.4945 2106.1974 1905.6315 2175.271 5542.645
#> n1e4 12075.252 16136.9870 20045.2995 18520.0205 21594.306 81975.030
#> n1e5 280937.762 313638.9725 385689.8809 377507.4770 436510.570 650410.745
#> neval cld
#> 100 a
#> 100 a
#> 100 b
#> 100 c
autoplot(result)
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: microseconds
#> expr min lq mean median uq max neval
#> p5 807.581 951.818 1229.734 1049.581 1246.138 5289.128 100
#> p25 3071.042 3425.274 5518.968 3677.548 4428.983 148454.424 100
#> p100 23622.538 29848.198 36246.281 34209.567 39206.094 80478.561 100
#> p400 276307.446 342264.559 417515.948 377826.551 458871.338 911453.001 100
#> 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.