RANK-BASED INFERENCE FOR BIVARIATE EXTREME-VALUE COPULAS

• 成果类型: Article
• 署名作者: Genest, Christian; Segers, Johan
• 署名单位: Laval University; Universite Catholique Louvain; Tilburg University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS672
• 发表日期: 2009
• 页码: 2990-3022
• 关键词: nonparametric-estimation; dependence-function; estimators; BEHAVIOR

摘要

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.