A Class of Asymptotically Unbiased Semi-parametric Estimators of the Tail Index

• Autores: M. Ivette Gomes, Frederico Caeiro
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 11, Nº. 2, 2002, págs. 345-364
• Idioma: inglés
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• Resumen

  • In this paper we consider a class of consistent semi-parametric estimators of a positive tail index $\gamma$, parameterized in 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 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.