The Annals of Statistics

Refined Pickands estimators of the extreme value index

Holger Drees

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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.

Article information

Source
Ann. Statist., Volume 23, Number 6 (1995), 2059-2080.

Dates
First available in Project Euclid: 15 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1034713647

Digital Object Identifier
doi:10.1214/aos/1034713647

Mathematical Reviews number (MathSciNet)
MR1389865

Zentralblatt MATH identifier
0883.62036

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties 62G30: Order statistics; empirical distribution functions

Keywords
Extreme value index tail index refined Pickands estimator Pickands process asymptotic normality robustness moment estimator

Citation

Drees, Holger. Refined Pickands estimators of the extreme value index. Ann. Statist. 23 (1995), no. 6, 2059--2080. doi:10.1214/aos/1034713647. https://projecteuclid.org/euclid.aos/1034713647


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