SCAD-penalized regression in high-dimensional partially linear models

Xie Huiliang, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

109 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)673-696
Number of pages24
JournalAnnals of Statistics
Volume37
Issue number2
DOIs
Publication statusPublished - 1 Apr 2009
Externally publishedYes

Keywords

  • Asymptotic normality
  • High-dimensional data
  • Oracle property
  • Penalized estimation
  • Semiparametric models
  • Variable selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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