Refined pickands estimators wtth bias correction

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 k_n largest order statistics. It was shown that under certain second order conditions on F the estimator is asymptotically biased if k_n 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 k_n.

Keywords:

• univariate extreme value distribution
• extreme value index
• choice of fraction of largest order statistics
• mixed Pickands estimator
• refined Pickands estimator
• bias correction
• robustness