Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations
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2017-03-01
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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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Villa, C (2017). Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations. Test, 26(1). pp. 95–118. 10.1007/s11749-016-0501-7 Retrieved from https://hdl.handle.net/10161/33565.
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Cristiano Villa
Prof. Cristiano Villa main research area is in Bayesian statistics, with particular interest in objective methods. His output has been published in several peer-reviewed journals and presented at international conferences, such as the ISBA International Conference, the O-Bayes conference, and the ERCIM conference. In addition to his research, Prof. Villa is deeply committed to teaching and enjoys interacting with students. His teaching interests include probability, statistics, linear modelling, and risk management. Before joining Duke Kunshan University (DKU), Prof. Villa was a member of the Newcastle University (UK) and the University of Kent (UK). Prior to joining academia in 2014, he worked as an auditor and as an advisor for KPMG in several countries, including, Italy, UK, New Zealand, and Singapore. He holds an M.Sc. and a Ph.D. from the University of Kent, UK.
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