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

C. Genest , Ivan Kojadinovic (1) , J. Nešlehová , J. Yan (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Center for Human Genetics, University of Leuven School of Medicine

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. © 2011 ISI/BS.

Domaines: Probabilités [math.PR]

C. Genest, Ivan Kojadinovic, J. Nešlehová, J. Yan. A goodness-of-fit test for bivariate extreme-value copulas. Bernoulli, 2011, 17 (1), pp.253-275. ⟨10.3150/10-BEJ279⟩. ⟨hal-00865060⟩