This paper proposes a new rank-based test of extreme-value dependence. The procedure is based on the first three moments of the bivariate probability integral transform of the underlying copula. It is seen that the test statistic is asymptotically normal and its finite- and large-sample variance are calculated explicitly. Consistent plug-in estimators for the variance are proposed, and a fast algorithm for their computation is given. Although it is shown via counterexamples that no test based on the probability integral transform can be consistent, the proposed procedure achieves good power against common alternatives, both in finite samples and asymptotically.
Bibliographical noteFunding Information:
Grants from the Natural Sciences and Engineering Research Council and the Fonds québécois de la recherche sur la nature et les technologies are gratefully acknowledged.
- Extreme-value copula
- Ghoudi-Khoudraji-Rivest test
- Kendall's distribution
- Kendall's tau
- Test of extremeness