## Bernoulli

• Bernoulli
• Volume 20, Number 2 (2014), 604-622.

### Information bounds for Gaussian copulas

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 20, Number 2 (2014), 604-622.

Dates
First available in Project Euclid: 28 February 2014

https://projecteuclid.org/euclid.bj/1393593999

Digital Object Identifier
doi:10.3150/12-BEJ499

Mathematical Reviews number (MathSciNet)
MR3178511

Zentralblatt MATH identifier
1321.62054

#### Citation

Hoff, Peter D.; Niu, Xiaoyue; Wellner, Jon A. Information bounds for Gaussian copulas. Bernoulli 20 (2014), no. 2, 604--622. doi:10.3150/12-BEJ499. https://projecteuclid.org/euclid.bj/1393593999

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