Open Access
2016 Bayesian inference for the extremal dependence
Giulia Marcon, Simone A. Padoan, Isadora Antoniano-Villalobos
Electron. J. Statist. 10(2): 3310-3337 (2016). DOI: 10.1214/16-EJS1162


A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The prior is extended to the polynomial degree, making our approach nonparametric. Although the analytical expression of the posterior is unknown, inference is possible via a trans-dimensional MCMC scheme. We show the efficiency of the proposed methodology by means of a simulation study. The extremal behaviour of log-returns of daily exchange rates between the Pound Sterling vs the U.S. Dollar and the Pound Sterling vs the Japanese Yen is analysed for illustrative purposes.


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Giulia Marcon. Simone A. Padoan. Isadora Antoniano-Villalobos. "Bayesian inference for the extremal dependence." Electron. J. Statist. 10 (2) 3310 - 3337, 2016.


Received: 1 December 2015; Published: 2016
First available in Project Euclid: 16 November 2016

zbMATH: 1357.62213
MathSciNet: MR3572851
Digital Object Identifier: 10.1214/16-EJS1162

Primary: 62G05 , 62G07 , 62G32

Keywords: Angular measure , Bayesian nonparametrics , Bernstein polynomials , exchange rates , Extremal dependence , Generalised extreme value distribution , max-stable distribution , trans-dimensional MCMC

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.10 • No. 2 • 2016
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