EstPhiNestedGumbel

library(VecDep)

First, let us fix some parameters.

q = 4
dim = c(2,2)
n = 1000

Construct a four dimensional hierarchical Gumbel copula with parameters (theta_0,theta_1,theta_2) = (2,3,4)

hac = gethac(dim,c(2,3,4),type = 1)

Draw a sample of size n from the copula

sample = suppressWarnings(HAC::rHAC(n,hac))
#> [1] "X1 <-> 1"
#> [1] "X2 <-> 2"
#> [1] "X3 <-> 3"
#> [1] "X4 <-> 4"

Estimate the mutual information between two random vectors of size two via pseudo maximum likelihood estimation

estphi(sample,dim,list("hac",type = 1,M = 10000),function(t){t * log(t)})
#> Warning in hac2nacopula(hac): NAs introduced by coercion
#> [1] "X1 <-> 1"
#> [1] "X2 <-> 2"
#> [1] "X3 <-> 3"
#> [1] "X4 <-> 4"
#> [1] 0.4854667