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We consider the problem of simultaneous variable selection and estimation inadditive, partially linear models for longitudinal/clustered data. We proposean estimation procedure via polynomial splines to estimate the nonparametriccomponents and apply proper penalty functions to achieve sparsity in the linearpart. Under reasonable conditions, we obtain the asymptotic normality of theestimators for the linear components and the consistency of the estimators forthe nonparametric components. We further demonstrate that, with proper choiceof the regularization parameter, the penalized estimators of the non-zerocoefficients achieve the asymptotic oracle property. The finite sample behaviorof the penalized estimators is evaluated with simulation studies andillustrated by a longitudinal CD4 cell count data set.

Simultaneous variable selection and estimation in semiparametric modeling of longitudinal/clustered data