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December 1995 Refined Pickands estimators of the extreme value index
Holger Drees
Ann. Statist. 23(6): 2059-2080 (December 1995). DOI: 10.1214/aos/1034713647

Abstract

Consider a distribution function that belongs to the weak domain of attraction of an extreme value distribution. The extreme value index $\beta$ will be estimated by mixtures of Pickands estimators, where the weights are generated by a probability measure which satisfies a certain integrability condition. We prove a functional limit theorem for a process of Pickands estimators and asymptotic normality of the refined Pickands estimator. For negative $\beta$ the new estimator is asymptotically superior to previously defined estimators. A simulation study also demonstrates the good small-sample performance. In particular, the estimator proves to be robust against an inappropriate choice of the number of upper order statistics used for estimation.

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Holger Drees. "Refined Pickands estimators of the extreme value index." Ann. Statist. 23 (6) 2059 - 2080, December 1995. https://doi.org/10.1214/aos/1034713647

Information

Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0883.62036
MathSciNet: MR1389865
Digital Object Identifier: 10.1214/aos/1034713647

Subjects:
Primary: 62G05
Secondary: 62G20, 62G30

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 6 • December 1995
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