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February 2011 Focused information criterion and model averaging for generalized additive partial linear models
Xinyu Zhang, Hua Liang
Ann. Statist. 39(1): 174-200 (February 2011). DOI: 10.1214/10-AOS832


We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.


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Xinyu Zhang. Hua Liang. "Focused information criterion and model averaging for generalized additive partial linear models." Ann. Statist. 39 (1) 174 - 200, February 2011.


Published: February 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1209.62088
MathSciNet: MR2797843
Digital Object Identifier: 10.1214/10-AOS832

Primary: 62G08
Secondary: 62G20 , 62G99

Keywords: Additive models , backfitting , focus parameter , generalized partially linear models , marginal integration , model average , Model selection , polynomial spline , shrinkage methods

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 1 • February 2011
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