Frederico Caeiro

Citation:

Caeiro, F., & Gomes I. M. (2002).  A class of asymptotically unbiased semi-parametric estimators of the tail index.. Test. 11, 345-364., Number 2

Abstract:

{Summary: We consider a class of consistent semi-parametric estimators of a positive tail index $\gamma$, parameterized by a tuning or control parameter $\alpha$. Such a control parameter enables us to have access, for any available sample, to an estimator of $\gamma$ with a null dominant component of asymptotic bias, and with a reasonably flat mean squared error pattern, as a function of $k$, the number of top order statistics considered. Moreover, we are able to achieve a high efficiency relative to the classical Hill estimator [ıt B. M. Hill}, Ann. Stat. 3, 1163–1174 (1975; Zbl 0323.62033)], provided we may have access to a larger number of top order statistics than the number needed for optimal estimation through the Hill estimator.}

Notes:

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