Testing independence for Archimedean copula based on Bernstein estimate of Kendall distribution function

In this study, we estimate the Kendall distribution function (K(t)) for Archimedean copula family using Bernstein polynomial approximation and we investigate its performance by Monte Carlo simulation. Then, we introduce a nonparametric test of independence which is based on Cramér–von-Mises distance of the new estimate of Kendall distribution function. Also, we examine the power and the size of the test and we compare it with the classical nonparametric test that is based on the empirical Kendall distribution function.