Hoff, Peter D.; Niu, Xiaoyue; Wellner, Jon A. Information bounds for Gaussian copulas. (English) Zbl 1321.62054 Bernoulli 20, No. 2, 604-622 (2014). Summary: Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are invariant to changes in the univariate marginal distributions, rank-based estimators are natural candidates for semiparametric copula estimation. Asymptotic information bounds for such estimators can be obtained from an asymptotic analysis of the rank likelihood, that is, the probability of the multivariate ranks. In this article, we obtain limiting normal distributions of the rank likelihood for Gaussian copula models. Our results cover models with structured correlation matrices, such as exchangeable or circular correlation models, as well as unstructured correlation matrices. For all Gaussian copula models, the limiting distribution of the rank likelihood ratio is shown to be equal to that of a parametric likelihood ratio for an appropriately chosen multivariate normal model. This implies that the semiparametric information bounds for rank-based estimators are the same as the information bounds for estimators based on the full data, and that the multivariate normal distributions are least favorable. Cited in 6 Documents MSC: 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62H12 Estimation in multivariate analysis 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid References: [1] Barnard, G.A. (1963). Logical aspects of the fiducial argument. Bull. Inst. Internat. Statist. 40 870-883. · Zbl 0137.12404 [2] Begun, J.M., Hall, W.J., Huang, W.M. and Wellner, J.A. 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