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

TL;DR

This paper introduces a method for simultaneous variable selection and estimation in additive partially linear models for longitudinal data, using polynomial splines and penalty functions to identify relevant variables and estimate their effects.

Contribution

It develops a novel estimation procedure combining spline approximation and penalization, achieving asymptotic normality, consistency, and oracle properties for the estimators.

Findings

Estimators are asymptotically normal for linear components.

Nonparametric estimators are consistent.

Penalized estimators achieve oracle property with proper regularization.

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 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.