Asymptotically unbiased estimators for the extreme-value index

Estimators of the extreme-value index are based on a set of upper order statistics. When the number of upper-order statistics used in the estimation of the extreme-value index is small, the variance of the estimator will be large. On the other hand, the use of a large number of upper statistics will introduce a big bias. There are several papers concerning how to balance the variance component and the bias component. In this paper, we give an unbiased estimator even if one uses a large number of upper-order statistics.