Frederico Caeiro

Citation:

Caeiro, F., Gomes M. I., & Pestana D. (2005).  Direct reduction of bias of the classical Hill estimator.. REVSTAT. 3, 113-136., Number 2

Abstract:

{Summary: We are interested in an adequate estimation of the dominant component of the bias of ıt B. M. Hill}\,'s estimator [Ann. Stat. 3, 1163–1174 (1975; Zbl 0323.62033)] of a positive tail index $\gamma$, in order to remove it from the classical Hill estimator in different asymptotically equivalent ways. If the second order parameters in the bias are computed at an adequate level $k_1$ of a larger order than that of the level $k$ at which the Hill estimator is computed, there may be no change in the asymptotic variances of these reduced bias tail index estimators, which are kept equal to the asymptotic variance of the Hill estimator, i.e., equal to $\gamma^2$. The asymptotic distributional properties of the proposed estimators of $\gamma$ are derived and the estimators are compared not only asymptotically, but also for finite samples through Monte Carlo techniques.}

Notes:

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