BIAS CORRECTION IN MULTIVARIATE EXTREMES

• 成果类型: Article
• 署名作者: Fougeres, Anne-Laure; de Haan, Laurens; Mercadier, Cecile
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1305
• 发表日期: 2015
• 页码: 903-934
• 关键词: pickands dependence; tail dependence; estimators; index; probability; statistics; models

摘要

The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this paper under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbiased versions of the empirical estimator introduced by Huang [Statistics of bivariate extremes (1992) Erasmus Univ.]. Since the new estimators have a regular behavior with respect to the number of observations, it is possible to deduce aggregated versions so that the choice of the threshold is substantially simplified. An extensive simulation study is provided as well as an application on real data.