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

J. Beirlant, G. Maribe and A. Verster

Insurance: Mathematics and Economics, 2018, vol. 78, issue C, 114-122

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 exhibits heavy censoring.

Keywords: Extreme value index; Pareto-type; Tail estimation; Random censoring; Bias reduction (search for similar items in EconPapers)
Date: 2018
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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