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

作者：Genest Christian^*; Kojadinovic Ivan; Neslehova Johanna; Yan Jun

来源：Bernoulli, 2011, 17(1): 253-275.

DOI：10.3150/10-BEJ279

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

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 fatuity. The test is based on a Cramer-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.

• 出版日期2011-2