• Bernoulli
  • Volume 17, Number 1 (2011), 253-275.

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

Christian Genest, Ivan Kojadinovic, Johanna Nešlehová, and Jun Yan

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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 Cramér–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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Bernoulli, Volume 17, Number 1 (2011), 253-275.

First available in Project Euclid: 8 February 2011

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extreme-value copula goodness of fit parametric bootstrap Pickands dependence function rank-based inference


Genest, Christian; Kojadinovic, Ivan; Nešlehová, Johanna; Yan, Jun. A goodness-of-fit test for bivariate extreme-value copulas. Bernoulli 17 (2011), no. 1, 253--275. doi:10.3150/10-BEJ279.

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