Quatrième séminaire de statistique – A08

Le jeudi 2 octobre 2008, à 13 h 30,
à la salle 1240 du pavillon Alexandre-Vachon

Fast Goodness-of-Fit Tests for Copulas

par

Jun Yan,
Department of statistics, University of Connecticut, Storrs

Résumé:
Goodness-of-fit tests are a fundamental element in the copula-based modeling of multivariate continuous distributions. Among the different procedures proposed in the literature, recent large scale simulations suggest that one of the most powerful tests is based on the empirical process arising from the comparison of the so-called empirical copula with a parametric estimate of the copula derived under the null hypothesis. As for most of the currently available goodness-of-fit procedures for copula models, the null distribution of the statistic for the latter test is obtained through the so-called parametric bootstrap. The main inconvenience of this approach is its very high computational cost, which, as the sample size increases, can be regarded as an obstacle to its application. In this work, fast procedures for assessing goodness of fit are obtained by means of an approximation of the weak limit of the empirical process under consideration, which can be rapidly simulated using multiplier central limit theorems. The resulting procedures are observed to be up to order 1000 times faster than the currently available parametric bootstrap procedures. Large scale Monte Carlo experiments, involving six frequently used parametric copula families, show that the proposed procedures provide a valid, much faster alternative to the parametric bootstrap. The suggested approach can be straightforwardly adapted to goodness-of-fit testing in multivariate parametric models. The application of the tests is illustrated through the modeling of a well-known insurance data set. The proposed procedures are expected to increase the practical applicability of goodness-of-fit testing in the copula-based modeling of multivariate continuous distributions.