The Annals of Statistics

Estimation and testing for partially linear single-index models

Hua Liang, Xiang Liu, Runze Li, and Chih-Ling Tsai

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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.

Article information

Ann. Statist. Volume 38, Number 6 (2010), 3811-3836.

First available in Project Euclid: 30 November 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G10: Hypothesis testing 62G20: Asymptotic properties 62J02: General nonlinear regression 62F12: Asymptotic properties of estimators

Efficiency hypothesis testing local linear regression nonparametric regression profile likelihood SCAD


Liang, Hua; Liu, Xiang; Li, Runze; Tsai, Chih-Ling. Estimation and testing for partially linear single-index models. Ann. Statist. 38 (2010), no. 6, 3811--3836. doi:10.1214/10-AOS835.

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