All the tests were done on an Arch Linux x86_64 machine with an Intel(R) Core(TM) i7 CPU (1.90GHz).
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
,
and simulate the parameter value and
matrices using rnorm()
. In order to ensure convergence with
a large
,
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 neval
#> n1e2 452.394 480.847 584.1662 496.792 545.262 5342.134 100
#> n1e3 1174.021 1401.068 2335.1833 1480.862 1632.074 71679.459 100
#> n1e4 10704.276 12985.917 14564.7576 14971.992 15825.298 21564.293 100
#> n1e5 167806.739 204826.742 238350.7291 231367.897 259028.736 339755.596 100
#> cld
#> a
#> a
#> b
#> c
autoplot(result)
Increasing the number of parameters
This time we fix the number of observations at , 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 732.366 757.488 798.6717 790.935 835.243 909.567 100
#> p25 2903.095 2925.156 3056.6724 2949.862 3016.091 8085.471 100
#> p100 23376.864 25868.997 28081.8670 26710.607 30829.069 49931.525 100
#> p400 266781.732 292708.517 326423.1932 312793.054 341474.797 574291.591 100
#> 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.