Layered Hill estimator for extreme data in clusters

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.