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Activity Number: 587
Type: Topic Contributed
Date/Time: Thursday, August 6, 2009 : 10:30 AM to 12:20 PM
Sponsor: Business and Economic Statistics Section
Abstract - #303873
Title: Properties and Uses of the Empirical Copula Process
Author(s): Christian Genest*+
Companies: Université Laval
Address: Département de mathématiques et de statistique, Québec, QC, G1V 0A6, Canada
Keywords: Asymptotics ; copula ; covariance ; dependence ordering ; empirical process ; ranks
Abstract:

The empirical copula process governs the stochastic behavior of rank-based statistics and inference procedures for copula models. Its large-sample limit was originally derived by Rüschendorf (1976) and was further studied, e.g., by Deheuvels (1979), Stute (1984), Fermanian et al. (2004) and Tsukahara (2005). A serial version of the process and a Möbius decomposition thereof were also considered by Genest & Rémillard (2004). Additional properties and extensions of the empirical copula process will be presented. Conditions will be given under which it has a smaller asymptotic covariance than the empirical process based on a random sample from the underlying copula. Consequences of this fact will be highlighted. The case of count data will also be touched upon. This talk is based on joint work with Johanna Neslehová, Bruno Rémillard, and Johan Segers.

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