Open Access
October 2009 Rank-based inference for bivariate extreme-value copulas
Christian Genest, Johan Segers
Ann. Statist. 37(5B): 2990-3022 (October 2009). DOI: 10.1214/08-AOS672


Consider a continuous random pair (X, Y) whose dependence is characterized by an extreme-value copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickands [Bull. Inst. Internat. Statist. 49 (1981) 859–878] and Capéraà, Fougères and Genest [Biometrika 84 (1997) 567–577]. In this paper, rank-based versions of these estimators are proposed for the more common case where the margins of X and Y are unknown. Results on the limit behavior of a class of weighted bivariate empirical processes are used to show the consistency and asymptotic normality of these rank-based estimators. Their finite- and large-sample performance is then compared to that of their known-margin analogues, as well as with endpoint-corrected versions thereof. Explicit formulas and consistent estimates for their asymptotic variances are also given.


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Christian Genest. Johan Segers. "Rank-based inference for bivariate extreme-value copulas." Ann. Statist. 37 (5B) 2990 - 3022, October 2009.


Published: October 2009
First available in Project Euclid: 17 July 2009

zbMATH: 1173.62013
MathSciNet: MR2541453
Digital Object Identifier: 10.1214/08-AOS672

Primary: 62G05 , 62G32
Secondary: 62G20

Keywords: Asymptotic theory , copula , extreme-value distribution , nonparametric estimation , Pickands dependence function , rank-based inference

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5B • October 2009
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