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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)592-624
Number of pages33
JournalAnnals of Statistics
Volume42
Issue number2
DOIs
StatePublished - Apr 2014

Keywords

  • Additive model
  • Group selection
  • Model selection
  • Oracle property
  • Partial linear models
  • Polynomial splines
  • Quadratic inference function
  • SCAD
  • Selection consistency

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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