First, let us fix some parameters.
Construct a four dimensional hierarchical Gumbel copula with parameters (theta_0,theta_1,theta_2) = (2,3,4)
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