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February 2011 A goodness-of-fit test for bivariate extreme-value copulas
Christian Genest, Ivan Kojadinovic, Johanna Nešlehová, Jun Yan
Bernoulli 17(1): 253-275 (February 2011). DOI: 10.3150/10-BEJ279

Abstract

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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Christian Genest. Ivan Kojadinovic. Johanna Nešlehová. Jun Yan. "A goodness-of-fit test for bivariate extreme-value copulas." Bernoulli 17 (1) 253 - 275, February 2011. https://doi.org/10.3150/10-BEJ279

Information

Published: February 2011
First available in Project Euclid: 8 February 2011

zbMATH: 1284.62331
MathSciNet: MR2797991
Digital Object Identifier: 10.3150/10-BEJ279

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

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Vol.17 • No. 1 • February 2011
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