A class of location invariant estimators for heavy tailed distributions

Abstract

In this paper, a new class of location-invariant semi-parametric estimators of a positive extreme value index $\gamma >0$ is proposed. Its asymptotic distributional representation and asymptotic normality are derived, and the optimal choice of the sample fraction by mean squared error is also discussed for some special cases. Finally comparison studies are provided for some familiar models by Monte Carlo simulations.

Keywords:

• Asymptotic normality
• location invariant heavy tailed index estimator
• second order regular variation

Mathematics Subject Classification:

• 60G70
• 62G32
• 62F12

Additional information

Funding

Project supported by NSFC (Grant No. 11571283) and the SWU Grant for Statistics Ph.D.