Bias-corrected geometric-type estimators of the tail index

Abstract

The estimation of the tail index is a central topic in extreme value analysis. We consider a geometric-type estimator for the tail index and study its asymptotic properties. We propose here two asymptotic equivalent bias-corrected geometric-type estimators and establish the corresponding asymptotic behaviour. We also apply the suggested estimators to construct asymptotic confidence intervals for this tail parameter. Some simulations in order to illustrate the finite sample behaviour of the proposed estimators are provided.