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Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models

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  • Li, Yujie
  • Li, Gaorong
  • Lian, Heng
  • Tong, Tiejun

Abstract

In this paper, we consider semiparametric varying coefficient partially linear models when the predictor variables of the linear part are ultra-high dimensional where the dimensionality grows exponentially with the sample size. We propose a profile forward regression (PFR) method to perform variable screening for ultra-high dimensional linear predictor variables. The proposed PFR algorithm can not only identify all relevant predictors consistently even for ultra-high semiparametric models including both nonparametric and parametric parts, but also possesses the screening consistency property. To determine whether or not to include the candidate predictor in the model of selected ones, we adopt an extended Bayesian information criterion (EBIC) to select the “best” candidate model. Simulation studies and a real data example are also carried out to assess the performance of the proposed method and to compare it with existing screening methods.

Suggested Citation

  • Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    • Handle: RePEc:eee:jmvana:v:155:y:2017:i:c:p:133-150
    DOI: 10.1016/j.jmva.2016.12.006
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    References listed on IDEAS

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    Cited by:

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    2. Zhang, Shen & Zhao, Peixin & Li, Gaorong & Xu, Wangli, 2019. "Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 37-52.
    3. Zhang, Xin & Zhao, Junlong, 2024. "Group variable selection via group sparse neural network," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).

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