ESTIMATION FOR A PARTIAL-LINEAR SINGLE-INDEX MODEL

• 成果类型: Article
• 署名作者: Wang, Jane-Ling; Xue, Liugen; Zhu, Lixing; Chong, Yun Sam
• 署名单位: University of California System; University of California Davis; Beijing University of Technology; Hong Kong Baptist University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS712
• 发表日期: 2010
• 页码: 246-274
• 关键词: sliced inverse regression; Dimension Reduction; convergence-rates; asymptotics

摘要

In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component of the model. Asymptotic normality is established for both parametric components. For the index, a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance. The estimator of the nonparametric link function achieves optimal convergence rates, and the structural error variance is obtained. In addition, the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters. A simulation study is performed and an application to a real dataset is illustrated. The extension to multiple indices is briefly sketched.