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
#> n1e2 472.719 571.7005 662.1916 613.9395 674.1195 1554.036
#> n1e3 1408.129 1769.0415 2138.9093 2028.5750 2251.4865 4869.616
#> n1e4 13616.880 18666.5195 22279.0953 21573.8380 24695.5150 47163.699
#> n1e5 281631.320 365871.8680 463930.8058 450246.9130 516867.2950 884133.441
#> neval cld
#> 100 a
#> 100 a
#> 100 a
#> 100 b
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: microseconds
#> expr min lq mean median uq max neval
#> p5 925.732 1056.840 1253.365 1117.012 1308.915 2779.369 100
#> p25 3669.131 4135.859 5436.506 4888.976 6507.479 11720.933 100
#> p100 34312.301 40968.241 47884.391 46110.473 53782.856 81330.025 100
#> p400 460696.228 536479.512 612616.016 587820.986 653332.783 936715.408 100
#> 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.