Geodesic
An asymptotically unbiased moment estimator of a negative extreme value index
Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 1, pp. 5-19

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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.
Keywords: extreme value index, semi-parametric estimation, moment estimator 
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Caeiro, Frederico; Gomes, M. An asymptotically unbiased moment estimator of a negative extreme value index. Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/DMPS_2010_30_1_a0/