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Variable selection for partially linear models via partial correlation

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  • Liu, Jingyuan
  • Lou, Lejia
  • Li, Runze

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.

Suggested Citation

  • Liu, Jingyuan & Lou, Lejia & Li, Runze, 2018. "Variable selection for partially linear models via partial correlation," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 418-434.
    • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:418-434
    DOI: 10.1016/j.jmva.2018.06.005
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, September.
    2. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
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    7. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, September.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Aifen Feng & Jingya Fan & Zhengfen Jin & Mengmeng Zhao & Xiaogai Chang, 2023. "Research Based on High-Dimensional Fused Lasso Partially Linear Model," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    2. Wang, Jia & Cai, Xizhen & Li, Runze, 2021. "Variable selection for partially linear models via Bayesian subset modeling with diffusing prior," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

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