Subsampling Extremes: From Block Maxima to Smooth Tail Estimation

TL;DR

This paper introduces a new tail index estimator based on subsample maxima that offers increased stability and simplicity over traditional Hill estimators, especially in threshold selection.

Contribution

The paper proposes a novel tail index estimator derived from subsample maxima, providing smoother sample paths and an intuitive threshold selection method.

Findings

Estimator has asymptotically smooth sample paths

It is more stable than the Hill estimator

Threshold selection is simplified without second-order fitting

Abstract

We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order statistics. The estimator presents multiple advantages over the Hill estimator. In particular, it has asymptotically smooth sample paths as a function of the threshold k, making it considerably more stable than the Hill estimator. The estimator also admits a simple and intuitive threshold selection rule that does not require fitting a second-order model. Journal of Multivariate Analysis, 130, 2014