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

2017/05/18 by Beirlant, Jan, Maribe, Gaonyalelwe, Verster, Andrehette · 3 citations
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.1705.06634

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.

Cited by

• Statistics of Extremes for the Insurance Industry
• Weighted Estimation of the Tail Index under Right Censorship: A Unified Approach Based on Kaplan-Meier and Nelson-Aalen Integrals
• Robust Tail Index Estimation under Random Censoring via Minimum Density Power Divergence

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