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Bayesian estimation of the tail index of a heavy tailed distribution under random censoring

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  • Ameraoui, Abdelkader
  • Boukhetala, Kamal
  • Dupuy, Jean-François

Abstract

Bayesian estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed for various prior distributions of the tail index. Convergence of the posterior distribution of the tail index to a Gaussian distribution is established. Finite-sample properties of the proposed estimators are investigated via simulations. Tail index estimation requires selecting an appropriate threshold for constructing relative excesses. A Monte Carlo procedure is proposed for tackling this issue. Finally, the proposed estimators are illustrated on a medical dataset.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:104:y:2016:i:c:p:148-168
    DOI: 10.1016/j.csda.2016.06.009
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    References listed on IDEAS

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    1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    2. Cabras, Stefano & Castellanos, María Eugenia, 2011. "A Bayesian Approach for Estimating Extreme Quantiles Under a Semiparametric Mixture Model," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 87-106, May.
    3. Zellner, Arnold, 1996. "Models, prior information, and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 75(1), pages 51-68, November.
    4. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
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    Cited by:

    1. 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.
    2. Kapil Kumar, 2018. "Classical and Bayesian estimation in log-logistic distribution under random censoring," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(2), pages 440-451, April.

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