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On the strong approximation of bootstrapped empirical copula processes with applications
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  • 作者：S. Bouzebda (12) salim.bouzebda@utc.fr
  • 关键词：multivariate Empirical Copula processes – ; strong invariance principles – ; kernel ; type estimator – ; Kiefer processes – ; Gaussian processes – ; change ; point detection – ; tests of independence.
  • 刊名：Mathematical Methods of Statistics
  • 出版年：2012
  • 出版时间：July 2012
  • 年：2012
  • 卷：21
  • 期：3
  • 页码：153-188
  • 全文大小：891.7 KB
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  • 作者单位：1. LMAC, Univ. Technologie de Compi茅gne, Compi茅gne, France2. LSTA, Univ. Pierre et Marie Curie, Paris, France
  • ISSN：1934-8045
文摘
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.

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