The Annals of Statistics
- Ann. Statist.
- Volume 42, Number 2 (2014), 592-624.
Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates
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.
Ann. Statist., Volume 42, Number 2 (2014), 592-624.
First available in Project Euclid: 20 May 2014
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Wang, Li; Xue, Lan; Qu, Annie; Liang, Hua. Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates. Ann. Statist. 42 (2014), no. 2, 592--624. doi:10.1214/13-AOS1194. https://projecteuclid.org/euclid.aos/1400592171
- Supplementary material: Supplement to “Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates”. The supplementary material provides a number of technical lemmas and their proofs. The technical lemmas are used in the proofs of Theorems 1–5 in the paper.