Some applications of the strong approximation of the integrated empirical copula processes

Abstract

The purpose of the present paper is to provide a strong invariance principle for the integrated empirical copula process [introduced in a series of papers by Henze and Nikitin in the univariate setting] with the rate of the approximation for multivariate empirical processes. The applications discussed here are change-point detection in multivariate copula models and the integrated empirical copula process with estimated parameter. Finally, a general notion of bootstrapped integrated empirical copula process, constructed by exchangeably weighting sample, is presented.