Abstract
In this paper, we study the behavior of the weighted quadratic functionals of the multivariate empirical copula processes under sequences of contiguous alternatives. The Karhunen-Loeve expansions of the corresponding limiting Gaussian processes are derived by using the results, in a series of papers, by Deheuvels, which are used to obtain the asymptotic distribution of the weighted multivariate Cramer-von Mises-type statistics. These results are applied to compute the relative local asymptotic efficiency of the considered statistics, in the spirit of Genest et al. (2006, 2007), and discuss briefly some aspects regarding the power of these statistical tests. Finally, we give some additional results concerning the integrated copula processes.
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