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.

Keywords:

• Asymptotic normality
• consistency
• Hill-type estimator

AMS 2000 Subject Classifications:

• Primary: 60G70
• Secondary: 62G32

Acknowledgments

The authors would like to thank the editor and the two referees for careful reading and comments which greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).