Refined Pickands estimators of the extreme value index
Open Access
- 1 December 1995
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 23 (6), 2059-2080
- https://doi.org/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.