The Annals of Statistics

Rank-based inference for bivariate extreme-value copulas

Christian Genest and Johan Segers

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Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 5B (2009), 2990-3022.

Dates
First available in Project Euclid: 17 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1247836675

Digital Object Identifier
doi:10.1214/08-AOS672

Mathematical Reviews number (MathSciNet)
MR2541453

Zentralblatt MATH identifier
1173.62013

Subjects
Primary: 62G05: Estimation 62G32: Statistics of extreme values; tail inference
Secondary: 62G20: Asymptotic properties

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

Citation

Genest, Christian; Segers, Johan. Rank-based inference for bivariate extreme-value copulas. Ann. Statist. 37 (2009), no. 5B, 2990--3022. doi:10.1214/08-AOS672. https://projecteuclid.org/euclid.aos/1247836675


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