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June 2007 Extending the rank likelihood for semiparametric copula estimation
Peter D. Hoff
Ann. Appl. Stat. 1(1): 265-283 (June 2007). DOI: 10.1214/07-AOAS107


Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula model, in which the associations among the variables are parameterized separately from their univariate marginal distributions. The purpose of this article is to provide a simple, general method of semiparametric inference for copula models via a type of rank likelihood function for the association parameters. The proposed method of inference can be viewed as a generalization of marginal likelihood estimation, in which inference for a parameter of interest is based on a summary statistic whose sampling distribution is not a function of any nuisance parameters. In the context of copula estimation, the extended rank likelihood is a function of the association parameters only and its applicability does not depend on any assumptions about the marginal distributions of the data, thus making it appropriate for the analysis of mixed continuous and discrete data with arbitrary marginal distributions. Estimation and inference for parameters of the Gaussian copula are available via a straightforward Markov chain Monte Carlo algorithm based on Gibbs sampling. Specification of prior distributions or a parametric form for the univariate marginal distributions of the data is not necessary.


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Peter D. Hoff. "Extending the rank likelihood for semiparametric copula estimation." Ann. Appl. Stat. 1 (1) 265 - 283, June 2007.


Published: June 2007
First available in Project Euclid: 29 June 2007

zbMATH: 1129.62050
MathSciNet: MR2393851
Digital Object Identifier: 10.1214/07-AOAS107

Keywords: Bayesian inference , latent variable model , marginal likelihood , Markov chain Monte Carlo , multivariate estimation , polychoric correlation , rank likelihood , sufficiency

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.1 • No. 1 • June 2007
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