Location invariant heavy tail index estimation with block method

Abstract

Motivated by the work of Qi [On the tail index of a heavy tailed distribution. Ann Inst Stat Math. 2010;62:277–298] and Fraga Alves [A location invariant Hill-type estimator. Extremes. 2001b;4:199–217], a new class of location invariant Hill-type estimators for heavy tail index is proposed. The weak consistency of the estimator is studied, the asymptotic expansion and limit distribution of the estimator are derived under second-order regular varying conditions. Simulation studies are performed to compare the new estimator with closely related estimators.