A class of unbiased location invariant Hill-type estimators for heavy tailed distributions

TL;DR

This paper introduces a new class of unbiased, location-invariant Hill-type estimators for heavy-tailed distributions, analyzing their asymptotic properties and optimal sample fraction selection through simulations.

Contribution

It develops a novel class of estimators building on previous methods, with detailed asymptotic analysis and practical guidelines for optimal sample fraction choice.

Findings

Establishes asymptotic normality of the estimators

Provides optimal sample fraction selection criteria

Demonstrates estimator performance via Monte Carlo simulations

Abstract

Based on the methods provided in Caeiro and Gomes (2002) and Fraga Alves (2001), a new class of location invariant Hill-type estimators is derived in this paper. Its asymptotic distributional representation and asymptotic normality are presented, and the optimal choice of 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.