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December 2010 Estimation and testing for partially linear single-index models
Hua Liang, Xiang Liu, Runze Li, Chih-Ling Tsai
Ann. Statist. 38(6): 3811-3836 (December 2010). DOI: 10.1214/10-AOS835


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.


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Hua Liang. Xiang Liu. Runze Li. Chih-Ling Tsai. "Estimation and testing for partially linear single-index models." Ann. Statist. 38 (6) 3811 - 3836, December 2010.


Published: December 2010
First available in Project Euclid: 30 November 2010

zbMATH: 1204.62068
MathSciNet: MR2766869
Digital Object Identifier: 10.1214/10-AOS835

Primary: 62G08
Secondary: 62F12 , 62G10 , 62G20 , 62J02

Keywords: efficiency , Hypothesis testing , local linear regression , Nonparametric regression , profile likelihood , SCAD

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 6 • December 2010
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