Tests of Independence Based on the Weighted Empirical Copula Process

A non-parametric test of independence between the components of a random vector based on the Cram\'{e}r-von Mises functional of the weighted empirical copula process is presented and its asymptotic behavior is derived. A closed-form expression of the test-statistic is provided for a number of weighting functions. Several issues relating to the choice of the weights are discussed, and a simulation study is conducted to investigate the power properties of the test in finite samples, where the test power is shown to be significantly affected by the choice of the weights.