On the comparison of several classical estimators of the extreme value index

Due to the fact that for heavy tails the classical Hill estimator of a positive extreme value index is asymptotically biased, new and interesting alternative estimators have appeared in the literature. In this work we compare several classical estimators of the extreme value index based on moments of the upper order statistics. Since several alternative estimators have eventually a null asymptotic bias, for some heavy tailed models, the comparison is performed not only with the Hill and recent generalized means estimators but also with an asymptotically unbiased Hill estimator. The comparison study is performed asymptotically, under a third-order framework, and for finite samples, through a Monte Carlo simulation study.