Simultaneous Variable Selection and Estimation in Semiparametric Modeling of Longitudinal/Clustered Data

• Activity Number: 322
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Shujie Ma*+ and Qiongxia Song and Lily Wang
• Companies: University of California at Riverside and The University of Texas at Dallas and The University of Georgia
• Keywords: clustered data ; longitudinal data ; model selection ; penalized least squares ; spline ; semi-parametric models

Abstract

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 nonzero 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 dataset.