Open Access
Translator Disclaimer
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


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.


Download Citation

Holger Drees. "Refined Pickands estimators of the extreme value index." Ann. Statist. 23 (6) 2059 - 2080, December 1995.


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

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

Primary: 62G05
Secondary: 62G20, 62G30

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
Back to Top