Bayesian Inference with M-splines on Spectral Measure of Bivariate Extremes

Khader Khadraoui () and Pierre Ribereau
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Khader Khadraoui: Laval University
Pierre Ribereau: Université Lyon 1

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 3, 765-788

Abstract: Abstract We consider a Bayesian methodology with M-splines for the spectral measure of a bivariate extreme-value distribution. The tail of a bivariate distribution function F in the max-domain of attraction of an extreme-value distribution function G may be approximated by that of its extreme value attractor. The function G is characterized by a probability measure with expectation equal to 1/2, called the spectral measure, and two extreme-value indices. This spectral measure determines the tail dependence structure of F. The approximation of the spectral measure is proposed thanks to a non-parametric Bayesian estimator that guarantees to fulfill a moment and a shape constraint. The problem of routine calculation of posterior distributions for both coefficients and knots of M-splines is addressed using the Markov chain Monte Carlo (MCMC) simulation technique of reversible jumps.

Keywords: Bayesian inference; M-splines; Bivariate extremes; Spectral measure; Monotone shape; Reversible-jumps MCMC; Primary 62G32; 62F15; 62G05; Secondary 62F30; 60J22; 65D07 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11009-019-09723-7

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