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April 2015 Bias correction in multivariate extremes
Anne-Laure Fougères, Laurens de Haan, Cécile Mercadier
Ann. Statist. 43(2): 903-934 (April 2015). DOI: 10.1214/14-AOS1305

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.

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Anne-Laure Fougères. Laurens de Haan. Cécile Mercadier. "Bias correction in multivariate extremes." Ann. Statist. 43 (2) 903 - 934, April 2015. https://doi.org/10.1214/14-AOS1305

Information

Published: April 2015
First available in Project Euclid: 23 March 2015

zbMATH: 1312.62061
MathSciNet: MR3325714
Digital Object Identifier: 10.1214/14-AOS1305

Subjects:
Primary: 62G05, 62G20, 62G32
Secondary: 60F05, 60G70

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 2 • April 2015
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