In this paper we consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the k largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of k. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample behaviour is obtained through Monte Carlo simulation.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1118,
author = {Frederico Caeiro and M. Ivette Gomes},
title = {An asymptotically unbiased moment estimator of a negative extreme value index},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {30},
year = {2010},
pages = {5-19},
zbl = {1208.62084},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1118}
}
Frederico Caeiro; M. Ivette Gomes. An asymptotically unbiased moment estimator of a negative extreme value index. Discussiones Mathematicae Probability and Statistics, Tome 30 (2010) pp. 5-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1118/
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