The Annals of Statistics

Refined Pickands estimators of the extreme value index

Holger Drees

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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

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

First available in Project Euclid: 15 October 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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