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
#> n1e2 449.207 482.098 588.0902 499.3605 544.9855 5519.103
#> n1e3 1189.696 1400.119 2370.4836 1495.0005 1652.0535 72293.328
#> n1e4 10790.825 13213.780 14673.8821 15050.4215 15921.9005 21236.888
#> n1e5 173501.197 209300.679 246166.4242 235537.5940 274855.6775 347349.453
#> neval cld
#> 100 a
#> 100 a
#> 100 b
#> 100 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 728.398 764.6845 805.918 785.6485 840.521 1100.08 100
#> p25 2894.383 2938.1395 3069.765 2962.1395 3035.295 8174.16 100
#> p100 23370.114 25888.4455 28260.419 26904.2230 30967.644 49765.34 100
#> p400 267196.812 292537.9520 326476.548 313191.7295 340923.560 572596.20 100
#> 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.