Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates

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.

Published in at http://dx.doi.org/10.1214/13-AOS1194 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Nonconcave penalized likelihood with a diverging number of parameters
• Variable selection in nonparametric additive models
• Estimation and variable selection for generalized additive partial linear models
• Simultaneous variable selection and estimation in semiparametric modeling of longitudinal/clustered data
• Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data

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• Sparse Partially Linear Additive Models
• Analysis of Deviance for Hypothesis Testing in Generalized Partially Linear Models
• Greedy Forward Regression for Variable Screening
• Fast Bayesian Inference in Nonparametric Double Additive Location-Scale Models With Right- and Interval-Censored Data