Trimmed extreme value estimators for censored heavy-tailed data

TL;DR

This paper introduces a novel trimming approach for censored heavy-tailed data that improves the estimation of extreme value indices and quantiles, with adaptive selection and strong empirical performance.

Contribution

It proposes a new kernel-based estimator with an adaptive trimming method for censored heavy-tailed data, enhancing estimation accuracy over existing methods.

Findings

The new kernel estimators outperform existing alternatives in simulations.

Adaptive trimming reduces bias and variance in extreme value estimation.

Application to insurance data demonstrates practical effectiveness.

Abstract

We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is applied to the state-of-the-art estimators for randomly right-censored tail estimators. Through an averaging procedure over the amount of trimming we derive new kernel type estimators. Extensive simulation suggests that one of the new considered kernels leads to a highly competitive estimator against virtually any other available alternative in this framework. Moreover, we propose an adaptive selection method for the amount of top data used in estimation based on the trimming procedure minimizing the asymptotic mean squared error. We also provide an illustration of this approach to simulated as well as to real-world MTPL insurance data.