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

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  • Beirlant, J.
  • Maribe, G.
  • Verster, A.

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.

Suggested Citation

  • Beirlant, J. & Maribe, G. & Verster, A., 2018. "Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 114-122.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:114-122
    DOI: 10.1016/j.insmatheco.2017.11.008
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    References listed on IDEAS

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    1. Ameraoui, Abdelkader & Boukhetala, Kamal & Dupuy, Jean-François, 2016. "Bayesian estimation of the tail index of a heavy tailed distribution under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 148-168.
    2. Gomes, M. Ivette & Oliveira, Orlando, 2003. "Censoring estimators of a positive tail index," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 147-159, November.
    3. Beirlant, J. & Bardoutsos, A. & de Wet, T. & Gijbels, I., 2016. "Bias reduced tail estimation for censored Pareto type distributions," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 78-88.
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    Cited by:

    1. Saida Mancer & Abdelhakim Necir & Souad Benchaira, 2023. "Bias Reduction in Kernel Tail Index Estimation for Randomly Truncated Pareto-Type Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1510-1547, August.

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