The Annals of Statistics

Bias correction in multivariate extremes

Anne-Laure Fougères, Laurens de Haan, and Cécile Mercadier

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 43, Number 2 (2015), 903-934.

Dates
First available in Project Euclid: 23 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1427115291

Digital Object Identifier
doi:10.1214/14-AOS1305

Mathematical Reviews number (MathSciNet)
MR3325714

Zentralblatt MATH identifier
1312.62061

Subjects
Primary: 62G32: Statistics of extreme values; tail inference 62G05: Estimation 62G20: Asymptotic properties
Secondary: 60F05: Central limit and other weak theorems 60G70: Extreme value theory; extremal processes

Keywords
Multivariate extreme value theory tail dependence bias correction threshold choice

Citation

Fougères, Anne-Laure; de Haan, Laurens; Mercadier, Cécile. Bias correction in multivariate extremes. Ann. Statist. 43 (2015), no. 2, 903--934. doi:10.1214/14-AOS1305. https://projecteuclid.org/euclid.aos/1427115291


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