Testing for Bivariate Extreme Dependence Using Kendall's Process


Jean-François Quessy, Département de mathématiques et informatique, Université du Québec à Trois-Rivières, P.B. 500, Trois-Rivières, Canada, G9A 5H7.
E-mail: jean-francois.quessy@uqtr.ca


Abstract.  New tests for the hypothesis of bivariate extreme-value dependence are proposed. All test statistics that are investigated are continuous functionals of either Kendall's process or its version with estimated parameters. The procedures considered are based on linear combinations of moments and on Cramér–von Mises distances. A suitably adapted version of the multiplier central limit theorem for Kendall's process enables the computation of asymptotically valid p-values. The power of the tests is evaluated for small, moderate and large sample sizes, as well as asymptotically, under local alternatives. An illustration with a real data set is presented.