SCAD-penalized regression in high-dimensional partially linear models

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.

Published in at http://dx.doi.org/10.1214/07-AOS580 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (6)

• High-dimensional graphs and variable selection with the Lasso
• Nonconcave penalized likelihood with a diverging number of parameters
• Asymptotic properties of bridge estimators in sparse high-dimensional regression models
• The sparsity and bias of the Lasso selection in high-dimensional linear regression
• High-dimensional generalized linear models and the lasso
• Variable selection using MM algorithms

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