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April 2014 Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates
Li Wang, Lan Xue, Annie Qu, Hua Liang
Ann. Statist. 42(2): 592-624 (April 2014). DOI: 10.1214/13-AOS1194

Abstract

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases statistical power for correlated data through incorporating the correlation information. A unique feature of the proposed method is its capability of handling model selection in cases where it is difficult to specify the likelihood function. We derive the quadratic inference function-based estimators for the linear coefficients and the nonparametric functions when the dimension of covariates diverges, and establish asymptotic normality for the linear coefficient estimators and the rates of convergence for the nonparametric functions estimators for both finite and high-dimensional cases. The proposed method and theoretical development are quite challenging since the numbers of linear covariates and nonlinear components both increase as the sample size increases. We also propose a doubly penalized procedure for variable selection which can simultaneously identify nonzero linear and nonparametric components, and which has an asymptotic oracle property. Extensive Monte Carlo studies have been conducted and show that the proposed procedure works effectively even with moderate sample sizes. A pharmacokinetics study on renal cancer data is illustrated using the proposed method.

Citation

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Li Wang. Lan Xue. Annie Qu. Hua Liang. "Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates." Ann. Statist. 42 (2) 592 - 624, April 2014. https://doi.org/10.1214/13-AOS1194

Information

Published: April 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1309.62077
MathSciNet: MR3210980
Digital Object Identifier: 10.1214/13-AOS1194

Subjects:
Primary: 62G08
Secondary: 62F12 , 62G10 , 62G20 , 62J02

Keywords: Additive model , group selection , Model selection , oracle property , partial linear models , polynomial splines , quadratic inference function , SCAD , selection consistency

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 2 • April 2014
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