Bernoulli

  • 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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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.

Article information

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

Dates
First available in Project Euclid: 8 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1297173842

Digital Object Identifier
doi:10.3150/10-BEJ279

Mathematical Reviews number (MathSciNet)
MR2797991

Zentralblatt MATH identifier
1284.62331

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

Citation

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. https://projecteuclid.org/euclid.bj/1297173842.


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