On the strong approximation of bootstrapped empirical copula processes with applications

Abstract

The purpose of the present paper is to provide a strong invariance principle for the generalized bootstrapped empirical copula processwith the rate of the approximation for multivariate empirical processes. As a by-product, we obtain a uniform-in-bandwidth consistency result for kernel-type estimators of copula derivatives, which is of its own interest. We introduce also the delta-sequence estimators of the copula derivatives. The applications discussed here are change-point detection in multivariate copula models, nonparametric tests of stochastic vectorial independence and the law of iterated logarithm for the generalized bootstrapped empirical copula process. Finally, a general notion of bootstrapped empirical copula process constructed by exchangeably weighting the sample is presented.