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.
Publié le : 1995-12-14
Classification:
Extreme value index,
tail index,
refined Pickands estimator,
Pickands process,
asymptotic normality,
robustness,
moment estimator,
62G05,
62G20,
62G30
@article{1034713647,
author = {Drees, Holger},
title = {Refined Pickands estimators of the extreme value index},
journal = {Ann. Statist.},
volume = {23},
number = {6},
year = {1995},
pages = { 2059-2080},
language = {en},
url = {http://dml.mathdoc.fr/item/1034713647}
}
Drees, Holger. Refined Pickands estimators of the extreme value index. Ann. Statist., Tome 23 (1995) no. 6, pp. 2059-2080. http://gdmltest.u-ga.fr/item/1034713647/