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Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations

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  • Cristiano Villa

    (University of Kent)

Abstract

In this paper, we discuss a method to define prior distributions for the threshold of a generalised Pareto distribution, in particular when its applications are directed to heavy-tailed data. We propose to assign prior probabilities to the order statistics of a given set of observations. In other words, we assume that the threshold coincides with one of the data points. We show two ways of defining a prior: by assigning equal mass to each order statistic, that is a uniform prior, and by considering the worth that every order statistic has in representing the true threshold. Both proposed priors represent a scenario of minimal information, and we study their adequacy through simulation exercises and by analysing two applications from insurance and finance.

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  • Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0501-7
    DOI: 10.1007/s11749-016-0501-7
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    References listed on IDEAS

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    1. C. Villa & S. G. Walker, 2015. "An Objective Approach to Prior Mass Functions for Discrete Parameter Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1072-1082, September.
    2. Fernández, C. & Steel, M.F.J., 1997. "On the Dangers of Modelling through Continuous Distributions : A Bayesian Perspective," Discussion Paper 1997-05, Tilburg University, Center for Economic Research.
    3. José Bernardo, 2005. "Intrinsic credible regions: An objective Bayesian approach to interval estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 317-384, December.
    4. J. L. Wadsworth & J. A. Tawn, 2012. "Likelihood-based procedures for threshold diagnostics and uncertainty in extreme value modelling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 543-567, June.
    5. P. Zea Bermudez & M. Turkman, 2003. "Bayesian approach to parameter estimation of the generalized pareto distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 259-277, June.
    6. Czado, Claudia & Delwarde, Antoine & Denuit, Michel, 2005. "Bayesian Poisson log-bilinear mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 260-284, June.
    7. L. Wasserman, 2000. "Asymptotic inference for mixture models by using data‐dependent priors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 159-180.
    8. Joan del castillo & Jalila Daoudi & Isabel Serra, 2012. "The full-tails gamma distribution applied to model extreme values," Papers 1211.0130, arXiv.org.
    9. 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.
    10. Donnelly, Catherine & Embrechts, Paul, 2010. "The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 1-33, May.
    11. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    12. MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
    13. Mendes, Beatriz Vaz de Melo & Lopes, Hedibert Freitas, 2004. "Data driven estimates for mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 583-598, October.
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    3. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.

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