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

Author

Listed:
  • Khader Khadraoui

    (Laval University)

  • Pierre Ribereau

    (Université Lyon 1)

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.

Suggested Citation

  • Khader Khadraoui & Pierre Ribereau, 2019. "Bayesian Inference with M-splines on Spectral Measure of Bivariate Extremes," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 765-788, September.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-019-09723-7
    DOI: 10.1007/s11009-019-09723-7
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    References listed on IDEAS

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