Modification of Moment-Based Tail Index Estimator: Sums versus Maxima

TL;DR

This paper introduces a new tail index estimator based on local maxima, extending previous moment-based methods for heavy-tailed data, and proves its consistency and asymptotic normality for independent data.

Contribution

It proposes a modified tail index estimator using local maxima, applicable for all positive tail indices, with theoretical validation of its statistical properties.

Findings

The new estimator is consistent for i.i.d. data.

It exhibits asymptotic normality under certain conditions.

Comparison with existing estimators is discussed.

Abstract

In this paper we continue the investigation of the SRCEN estimator of the extreme value index $\gamma$ (or the tail index $\alpha=1/\gamma$) proposed in \cite{MCE} for $\gamma>1/2$. We propose a new estimator based on the local maximum. This, in fact, is a modification of the SRCEN estimator to the case $\gamma>0$. We establish the consistency and asymptotic normality of the newly proposed estimator for i.i.d. data. Also, a short discussion on the comparison of the estimators is included.