Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas

Consider a random sample from a continuous multivariate distribution function F with copula C. In order to test the null hypothesis that C belongs to a certain parametric family, we construct an under H0 asymptotically distribution-free process that serves as a tests generator. The process is a transformation of the difference of a semi-parametric and a parametric estimator of C. This transformed empirical process converges weakly to a standard multivariate Wiener process, paving the way for a multitude of powerful asymptotically distribution-free goodness-of-fit tests for copula families. We investigate the finite-sample performance of our approach through a simulation study and illustrate its applicability with a data analysis.