Rank-based Inference for Bivariate Extreme-value Copulas
(2009) Annals of Statistics — Vol. 37, n° 5B, p. 2990-3022 (2009)
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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 Caperaa, Fougeres 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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Citations
Genest, C., & Segers, J. (2009). Rank-based Inference for Bivariate Extreme-value Copulas. Annals of Statistics, 37(5B), 2990-3022. https://doi.org/10.1214/08-AOS672 (Original work published 2009)