Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications

TL;DR

This paper introduces a new bias-reduced estimator for tail index in censored heavy-tailed data, improving accuracy in actuarial applications through bootstrap confidence intervals and simulation comparisons.

Contribution

It proposes a novel bias reduction method for extreme value index estimation in censored data, with a bootstrap approach for confidence intervals and application to insurance data.

Findings

New bias-reduced estimator outperforms existing methods in simulations

Bootstrap confidence intervals provide reliable uncertainty quantification

Application to insurance data demonstrates practical utility

Abstract

The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value index can be substantial and depends strongly on the amount of censoring. We review the available estimators, propose a new bias reduced estimator, and show how shrinkage estimation can help to keep the MSE under control. A bootstrap algorithm is proposed to construct confidence intervals. We compare these new proposals with the existing estimators through simulation. We conclude this paper with a detailed study of a long-tailed car insurance portfolio, which typically exhibit heavy censoring.