ESTIMATION AND TESTING FOR PARTIALLY LINEAR SINGLE-INDEX MODELS

• 成果类型: Article
• 署名作者: Liang, Hua; Liu, Xiang; Li, Runze; Tsai, Chih-Ling
• 署名单位: University of Rochester; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS835
• 发表日期: 2010
• 页码: 3811-3836
• 关键词: semiparametric estimation; profile likelihood; variable selection; regression; variance

摘要

In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the true model consistently. Finally, we develop a linear hypothesis test for the parametric coefficients and a goodness-of-fit test for the nonparametric component, respectively. Monte Carlo studies are also presented.