Open Access
May 2012 Bayesian estimation of a bivariate copula using the Jeffreys prior
Simon Guillotte, François Perron
Bernoulli 18(2): 496-519 (May 2012). DOI: 10.3150/10-BEJ345


A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its marginal distributions. We consider the problem of estimating the copula function and adopt a Bayesian approach. On the space of copula functions, we construct a finite-dimensional approximation subspace that is parametrized by a doubly stochastic matrix. A major problem here is the selection of a prior distribution on the space of doubly stochastic matrices also known as the Birkhoff polytope. The main contributions of this paper are the derivation of a simple formula for the Jeffreys prior and showing that it is proper. It is known in the literature that for a complex problem like the one treated here, the above results are difficult to obtain. The Bayes estimator resulting from the Jeffreys prior is then evaluated numerically via Markov chain Monte Carlo methodology. A rather extensive simulation experiment is carried out. In many cases, the results favour the Bayes estimator over frequentist estimators such as the standard kernel estimator and Deheuvels’ estimator in terms of mean integrated squared error.


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Simon Guillotte. François Perron. "Bayesian estimation of a bivariate copula using the Jeffreys prior." Bernoulli 18 (2) 496 - 519, May 2012.


Published: May 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1318.62112
MathSciNet: MR2922459
Digital Object Identifier: 10.3150/10-BEJ345

Keywords: Birkhoff polytope , copula , doubly stochastic matrices , finite mixtures , Jeffreys prior , Markov chain Monte Carlo , Metropolis-within-Gibbs sampling , nonparametric , objective Bayes

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability

Vol.18 • No. 2 • May 2012
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