Layered Hill estimator for extreme data in clusters

TL;DR

The paper introduces the layered Hill estimator, a robust method for estimating the tail exponent of heavy-tailed distributions, especially effective with missing extreme data, supported by theoretical and simulation evidence.

Contribution

It proposes a novel layered Hill estimator that improves robustness and accuracy over traditional methods for tail exponent estimation.

Findings

Layered Hill estimator outperforms traditional Hill estimator in robustness.

The estimator exhibits consistency and asymptotic normality.

Simulation studies confirm improved performance with missing extreme data.

Abstract

A new estimator is proposed for estimating the tail exponent of a heavy-tailed distribution. This estimator, referred to as the layered Hill estimator, is a generalization of the traditional Hill estimator, building upon a layered structure formed by clusters of extreme values. We argue that the layered Hill estimator provides a robust alternative to the traditional approach, exhibiting desirable asymptotic properties such as consistency and asymptotic normality for the tail exponent. Both theoretical analysis and simulation studies demonstrate that the layered Hill estimator shows significantly better and more robust performance, particularly when a portion of the extreme data is missing.