The Annals of Statistics
- Ann. Statist.
- Volume 39, Number 4 (2011), 1827-1851.
Estimation and variable selection for generalized additive partial linear models
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.
Ann. Statist., Volume 39, Number 4 (2011), 1827-1851.
First available in Project Euclid: 26 July 2011
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Backfitting generalized additive models generalized partially linear models LASSO nonconcave penalized likelihood penalty-based variable selection polynomial spline quasi-likelihood SCAD shrinkage methods
Wang, Li; Liu, Xiang; Liang, Hua; Carroll, Raymond J. Estimation and variable selection for generalized additive partial linear models. Ann. Statist. 39 (2011), no. 4, 1827--1851. doi:10.1214/11-AOS885. https://projecteuclid.org/euclid.aos/1311688537
- Supplementary material: Detailed proofs and additional simulation results of: Estimation and variable selection for generalized additive partial linear models. The supplemental materials contain detailed proofs and additional simulation results.