  We consider the problem of simultaneous variable selection and estimation in
additive, partially linear models for longitudinal/clustered data. We propose
an estimation procedure via polynomial splines to estimate the nonparametric
components and apply proper penalty functions to achieve sparsity in the linear
part. Under reasonable conditions, we obtain the asymptotic normality of the
estimators for the linear components and the consistency of the estimators for
the nonparametric components. We further demonstrate that, with proper choice
of the regularization parameter, the penalized estimators of the non-zero
coefficients achieve the asymptotic oracle property. The finite sample behavior
of the penalized estimators is evaluated with simulation studies and
illustrated by a longitudinal CD4 cell count data set.
