The Annals of Statistics

Focused information criterion and model averaging for generalized additive partial linear models

Xinyu Zhang and Hua Liang

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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.

Article information

Ann. Statist. Volume 39, Number 1 (2011), 174-200.

First available in Project Euclid: 3 December 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties 62G99: None of the above, but in this section

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


Zhang, Xinyu; Liang, Hua. Focused information criterion and model averaging for generalized additive partial linear models. Ann. Statist. 39 (2011), no. 1, 174--200. doi:10.1214/10-AOS832.

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