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We propose generalized additive partial linear models for complex data whichallow one to capture nonlinear patterns of some covariates, in the presence oflinear components. The proposed method improves estimation efficiency andincreases statistical power for correlated data through incorporating thecorrelation information. A unique feature of the proposed method is itscapability of handling model selection in cases where it is difficult tospecify the likelihood function. We derive the quadratic inferencefunction-based estimators for the linear coefficients and the nonparametricfunctions when the dimension of covariates diverges, and establish asymptoticnormality for the linear coefficient estimators and the rates of convergencefor the nonparametric functions estimators for both finite and high-dimensionalcases. The proposed method and theoretical development are quite challengingsince the numbers of linear covariates and nonlinear components both increaseas the sample size increases. We also propose a doubly penalized procedure forvariable selection which can simultaneously identify nonzero linear andnonparametric components, and which has an asymptotic oracle property.Extensive Monte Carlo studies have been conducted and show that the proposedprocedure works effectively even with moderate sample sizes. A pharmacokineticsstudy on renal cancer data is illustrated using the proposed method.

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