Variable selection for partially linear models via partial correlation

Jingyuan Liu, Lejia Lou, Runze Li

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

The partially linear model (PLM) is a useful semiparametric extension of the linear model that has been well studied in the statistical literature. This paper proposes a variable selection procedure for the PLM with ultrahigh dimensional predictors. The proposed method is different from the existing penalized least squares procedure in that it relies on partial correlation between the partial residuals of the response and the predictors. We systematically study the theoretical properties of the proposed procedure and prove its model consistency property. We further establish the root-n convergence of the estimator of the regression coefficients and the asymptotic normality of the estimate of the baseline function. We conduct Monte Carlo simulations to examine the finite-sample performance of the proposed procedure and illustrate the proposed method with a real data example.

Original languageEnglish (US)
Pages (from-to)418-434
Number of pages17
JournalJournal of Multivariate Analysis
Volume167
DOIs
StatePublished - Sep 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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