A class of semiparametric tail index estimators and its applications

A new class of semiparametric estimators of the tail index is proposed. These estimators are based on a rather general class of semiparametric statistics. Their asymptotic normality is proved. The new estimators are compared with several other recently introduced estimators of the tail index in terms of the asymptotic mean-square error. An algorithm to calculate the new estimators is developed and then applied to several real data sets.