Open Access
August 2011 Estimation and variable selection for generalized additive partial linear models
Li Wang, Xiang Liu, Hua Liang, Raymond J. Carroll
Ann. Statist. 39(4): 1827-1851 (August 2011). DOI: 10.1214/11-AOS885


We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration.


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Li Wang. Xiang Liu. Hua Liang. Raymond J. Carroll. "Estimation and variable selection for generalized additive partial linear models." Ann. Statist. 39 (4) 1827 - 1851, August 2011.


Published: August 2011
First available in Project Euclid: 26 July 2011

zbMATH: 1227.62053
MathSciNet: MR2893854
Digital Object Identifier: 10.1214/11-AOS885

Primary: 62G08
Secondary: 62G20 , 62G99

Keywords: backfitting , generalized additive models , generalized partially linear models , Lasso , nonconcave penalized likelihood , penalty-based variable selection , polynomial spline , quasi-likelihood , SCAD , shrinkage methods

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 4 • August 2011
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