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Bayesian copula selection. (English) Zbl 1157.62359
Summary: In recent years, the use of copulas has grown extremely fast and with it, the need for a simple and reliable method to choose the right copula family. Existing methods pose numerous difficulties and none is entirely satisfactory. We propose a Bayesian method to select the most probable copula family among a given set. The copula parameters are treated as nuisance variables, and hence do not have to be estimated. Furthermore, by a parameterization of the copula density in terms of Kendall’s \(\tau \), the prior on the parameter is replaced by a prior on \(\tau \), conceptually more meaningful. The prior on \(\tau \), common to all families in the set of tested copulas, serves as a basis for their comparison. Using simulated data sets, we study the reliability of the method and observe the following: (1) the frequency of successful identification approaches 100% as the sample size increases, (2) for weakly correlated variables, larger samples are necessary for reliable identification.

62F15 Bayesian inference
62H20 Measures of association (correlation, canonical correlation, etc.)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text: DOI
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