ASYMPTOTICALLY DISTRIBUTION-FREE GOODNESS-OF-FIT TESTING FOR TAIL COPULAS

• 成果类型: Article
• 署名作者: Can, Sami Umut; Einmahl, John H. J.; Khmaladze, Estate V.; Laeven, Roger J. A.
• 署名单位: University of Amsterdam; Tilburg University; Victoria University Wellington
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1304
• 发表日期: 2015
• 页码: 878-902
• 关键词: model checks; regression; estimator

摘要

Let (X-1, Y-1),..., (X-n, Y-n) be an i.i.d sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima V-i=1(n) X-i and V-i=1(n) Y-i is then characterized by the marginal extreme value indices and the tail copula R. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit tests for the tail copula R. The procedure is based on a transformation of a suitable empirical process derived from a semi-parametric estimator of R. The transformed empirical process converges weakly to a standard Wiener process, paving the way for a multitude of asymptotically distribution-free goodness-of-fit tests. We also extend our results to the m-variate (m > 2) case. In a simulation study we show that the limit theorems provide good approximations for finite samples and that tests based on the transformed empirical process have high power.