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April 2009 SCAD-penalized regression in high-dimensional partially linear models
Huiliang Xie, Jian Huang
Ann. Statist. 37(2): 673-696 (April 2009). DOI: 10.1214/07-AOS580

Abstract

We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be achieved simultaneously for the linear and nonparametric components. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to have the asymptotic oracle property, in the sense that it is asymptotically normal with the same means and covariances that they would have if the zero coefficients were known in advance. The finite sample behavior of the SCAD-penalized estimators is evaluated with simulation and illustrated with a data set.

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Huiliang Xie. Jian Huang. "SCAD-penalized regression in high-dimensional partially linear models." Ann. Statist. 37 (2) 673 - 696, April 2009. https://doi.org/10.1214/07-AOS580

Information

Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62037
MathSciNet: MR2502647
Digital Object Identifier: 10.1214/07-AOS580

Subjects:
Primary: 62G08, 62J05
Secondary: 62E20

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 2 • April 2009
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