Extending the rank likelihood for semiparametric copula estimation

By Peter D. Hoff. 2006

311 citations recorded by the source corpus.

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 method of semiparametric inference for copula models via the construction of what we call a marginal set 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 marginal set 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 margins. Estimation and inference for parameters of the Gaussian copula are available via a straightforward Markov chain Monte Carlo algorithm based on Gibbs sampling.

Subfields: Finance, Statistics and Probability

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Citations in the corpus

Causal Inference through a Witness Protection Program (2014, methodology): “We infer a Gaussian copula correlation matrix using the extended rank likelihood method of Hoff (2007) with the R package sbgcop, which can deal with discrete and continuous variables but requires expensive MCMC sampling.”
Gaussian Copula Marginal Regression (2012, methodology): “For an example of the latter use of copulas see the work on semiparametric Gaussian copula modelling by Hoff [23] and the references therein.”
Why Ordinal Variables Can (Almost) Always Be Treated as Continuous Variables: Clarifying Assumptions of Robust Continuous and Ordinal Factor Analysis Estimation Methods (2020, background): “Gaussian copula models pose a multivariate normal distribution for modeling the dependency structure while allowing a semiparametric estimation of the marginal distribution (Hoff, 2007; Gruhl et al., 2013; Murray et al., 2013).”
A hierarchical eigenmodel for pooled covariance estimation (2008, methodology): “One remedy to this situation, which was used by Hoff (2007a) in the context of sampling from the Bingham distribution, is to sample from the full conditional distribution of columns taken two at a time.”