Hoff, Peter D. Extending the rank likelihood for semiparametric copula estimation. (English) Zbl 1129.62050 Ann. Appl. Stat. 1, No. 1, 265-283 (2007). Summary: 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 functions 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. Cited in 1 ReviewCited in 47 Documents MSC: 62H12 Estimation in multivariate analysis 62G05 Nonparametric estimation 65C40 Numerical analysis or methods applied to Markov chains 65C60 Computational problems in statistics (MSC2010) 62H20 Measures of association (correlation, canonical correlation, etc.) Keywords:Bayesian inference; polychoric correlation; latent variables model; sufficiency; marginal likelihood Software:sbgcop PDFBibTeX XMLCite \textit{P. D. Hoff}, Ann. Appl. Stat. 1, No. 1, 265--283 (2007; Zbl 1129.62050) Full Text: DOI arXiv Euclid