Abstract
In this paper we consider a class of consistent semi-parametric estimators of a positive tail index γ, parameterized in atuning orcontrol parameter α. Such a control parameter enables us to have access, for any available sample, to an estimator of γ with a null dominant component of asymptotic bias, and with a reasonably flatMean Squared Error pattern, as a functional ofk, the number of top order statistics considered. Moreover, we are able to achieve a high efficiency relatively to the classical Hill estimator, provided we may have access to a larger number of top order statistics than the number needed for optimal estimation through the Hill estimator.
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Caeiro, F., Ivette Gomes, M. A class of asymptotically unbiased semi-parametric estimators of the tail index. Test 11, 345–364 (2002). https://doi.org/10.1007/BF02595711
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DOI: https://doi.org/10.1007/BF02595711