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A goodness-of-fit test for bivariate extreme-value copulas. (English) Zbl 1284.62331

Summary: 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 the first author and J. Segers [Ann. Stat. 37, No. 5B, 2990–3022 (2009; Zbl 1173.62013)]. 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.

MSC:

62H15 Hypothesis testing in multivariate analysis
62F10 Point estimation
62F40 Bootstrap, jackknife and other resampling methods
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas

Citations:

Zbl 1173.62013

Software:

copula; QRM; copula
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Full Text: DOI arXiv

References:

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