Inference for Covariate-Adjusted Semiparametric Gaussian Copula Model Using Residual Ranks

• Activity Number: 522 - Recent Advances in Semiparametric Statistical Methods
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yue Zhao* and Irene Gijbels and Ingrid Van Keilegom
• Companies: KU Leuven and KU Leuven and KU Leuven
• Keywords: Gaussian copula; normal scores rank correlation coefficient; residual rank; Spearman's rho; semiparametric efficiency

Abstract

We investigate the inference of the copula parameter in the semiparametric Gaussian copula model when the copula component, subject to the influence of a covariate, is only indirectly observed as the response in a linear regression model. We consider estimators based on residual ranks instead of the usual but unobservable oracle ranks. We first study two such estimators for the copula correlation matrix, one via inversion of Spearman's rho and the other via normal scores rank correlation coefficient. We show that these estimators are asymptotically equivalent to their counterparts based on the oracle ranks. Then, for the copula correlation matrix under constrained parametrizations, we show that the classical one-step estimator in conjunction with the residual ranks remains semiparametrically efficient for estimating the copula parameter. The accuracy of the estimators based on residual ranks is confirmed by simulation studies.