Refined pickands estimators wtth bias correction

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Abstract
Consider an univariate distribution function F that belongs to the weak domain of attraction of an extreme value distribution. In Drees (1994) mixtures of Pickands estimators of the extreme value index β were considered that are based on the kn largest order statistics. It was shown that under certain second order conditions on F the estimator is asymptotically biased if kn grows too fast. Here we introduce a quite general bias correcting procedure that allows to utilize more largest order statistics. Moreover, it is proven that the estimator yields sensible results even if some of the model assumptions are not satisfied. A simulation study demonstrates the robustness against an unsuitable choice of kn.