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

Cristiano Villa ()
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Cristiano Villa: University of Kent

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 1, No 5, 95-118

Abstract: 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.

Keywords: Extreme values; Generalised Pareto distribution; Heavy tails; Kullback–Leibler divergence; Self-information loss; Primary 62F15; Secondary 62P05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11749-016-0501-7

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