A goodness-of-fit test for bivariate extreme-value copulas

Details A goodness-of-fit test for bivariate extreme-value copulas A goodness-of-fit test for bivariate extreme-value copulas

2011-02-10

arxiv.org/abs/1102.2078v1

Bernoulli 2011, Vol. 17, No. 1, 253-275

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ279 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ279

It is often reasonable to assume that the dependence structure of a bivariate continuous distribution belongs to the class of extreme-value copulas. The latter are characterized by their Pickands dependence function. In this paper, a procedure is proposed for testing whether this function belongs to a given parametric family. The test is based on a Cram\'{e}r--von Mises statistic measuring the distance between an estimate of the parametric Pickands dependence function and either one of two nonparametric estimators thereof studied by Genest and Segers [Ann. Statist. 37 (2009) 2990--3022]. As the limiting distribution of the test statistic depends on unknown parameters, it must be estimated via a parametric bootstrap procedure, the validity of which is established. Monte Carlo simulations are used to assess the power of the test and an extension to dependence structures that are left-tail decreasing in both variables is considered.

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