SEMIPARAMETRIC GAUSSIAN COPULA MODELS: GEOMETRY AND EFFICIENT RANK-BASED ESTIMATION

• 成果类型: Article
• 署名作者: Segers, Johan; van den Akker, Ramon; Werker, Bas J. M.
• 署名单位: Universite Catholique Louvain; Tilburg University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1244
• 发表日期: 2014
• 页码: 1911-1940
• 关键词: bivariate survival-data; Graphical Models; parameters; regression; inference

摘要

We propose, for multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically efficient estimator for the Euclidean copula parameter. This estimator is defined as a one-step update of a rank-based pilot estimator in the direction of the efficient influence function, which is calculated explicitly. Moreover, finite-dimensional algebraic conditions are given that completely characterize efficiency of the pseudo-likelihood estimator and adaptivity of the model with respect to the unknown marginal distributions. For correlation matrices structured according to a factor model, the pseudo-likelihood estimator turns out to be semiparametrically efficient. On the other hand, for Toeplitz correlation matrices, the asymptotic relative efficiency of the pseudo-likelihood estimator can be as low as 20%. These findings are confirmed by Monte Carlo simulations. We indicate how our results can be extended to joint regression models.