PARAMETRIC COPULA ADJUSTED FOR NON- AND SEMIPARAMETRIC REGRESSION

• 成果类型: Article
• 署名作者: Zhao, Yue; Gijbels, Irene; Van Keilegom, Ingrid
• 署名单位: KU Leuven; KU Leuven; KU Leuven; University of York - UK
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2126
• 发表日期: 2022
• 页码: 754-780
• 关键词: nonparametric-estimation; efficient estimation; Empirical Process; models; RESIDUALS; inference

摘要

We consider a multivariate response regression model where each coordinate is described by a location-scale non- or semiparametric regression and where the dependence structure of the noise term is described by a parametric copula. Our goal is to estimate the associated Euclidean copula parameter, given a sample of the response and the covariate. In the absence of the copula sample, the usual oracle ranks are no longer computable. Instead, we study the normal scores estimator for the Gaussian copula and generalized pseudo-likelihood estimation for general parametric copulas, both based on residual ranks calculated from preliminary non- or semiparametric estimators of the location and scale functions. We show that the residual-based estimators are asymptotically equivalent to their oracle counterparts and provide explicit rate of convergence. Partially to serve this objective, we also study weighted convergence of the residual empirical process under the nonor semiparametric regression model.