This dataset is a simple test: we simulate random samples from a density inside the piecewise copula class, and test whether or not the estimator can recover it. For that, we will use a 2-dimensional sample with 500 observations, uniform on the unit hypercube, and apply the following function: $$h(u) = (u_1, \frac{u_2 + I_{u_1 \le \frac{1}{4}} + 2I_{u_1 \le \frac{1}{2}} + I_{\frac{3}{4} \le u_1}}{4})$$
recoveryourself_dataA matrix with 500 rows and 2 columns
The example section below gives the code to re-generate this data if needed.
This dataset is studied in O. Laverny, V. Maume-Deschamps, E. Masiello and D. Rullière (2020).
laverny2020cort
set.seed(seed = 12, kind = "Mersenne-Twister", normal.kind = "Inversion")
x = matrix(runif(1000),500,2)
recoveryourself_data = t(apply(x, 1,function(u){
if(u[1]< 1/4){
u[2] = 3/4 + u[2]/4
} else{ if(u[1]<1/2){
u[2] = 1/2 + u[2]/4
} else { if(u[1]<3/4){
u[2] = u[2]/4
} else {
u[2] = 1/4 + u[2]/4
}}}
return(u)
}))