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

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.

Published in at http://dx.doi.org/10.3150/11-BEJ386 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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• High-dimensional graphs and variable selection with the Lasso
• Properties of principal component methods for functional and longitudinal data analysis
• Variable selection in semiparametric regression modeling
• Spline-backfitted kernel smoothing of nonlinear additive autoregression model
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Cited by in corpus (4)

• Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates
• Two-step spline estimating equations for generalized additive partially linear models with large cluster sizes
• On Selection of Semiparametric Spatial Regression Models
• Sparse Model Identification and Learning for Ultra-high-dimensional Additive Partially Linear Models