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Semiparametric regression models with additive nonparametric components and high dimensional parametric components

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  • Du, Pang
  • Cheng, Guang
  • Liang, Hua

Abstract

This paper concerns semiparametric regression models with additive nonparametric components and high dimensional parametric components under sparsity assumptions. To achieve simultaneous model selection for both nonparametric and parametric parts, we introduce a penalty that combines the adaptive empirical L2-norms of the nonparametric component functions and the SCAD penalty on the coefficients in the parametric part. We use the additive partial smoothing spline estimate as the initial estimate and establish its convergence rate with diverging dimensions of parametric components. Our simulation studies reveal excellent model selection performance of the proposed method. An application to an economic study on Canadian household gasoline consumption reveals interesting results.

Suggested Citation

  • Du, Pang & Cheng, Guang & Liang, Hua, 2012. "Semiparametric regression models with additive nonparametric components and high dimensional parametric components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2006-2017.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2006-2017
    DOI: 10.1016/j.csda.2011.12.007
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    References listed on IDEAS

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    Cited by:

    1. Luo, June & Gerard, Patrick, 2013. "Using thresholding difference-based estimators for variable selection in partial linear models," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2601-2606.
    2. Guo, Jie & Tang, Manlai & Tian, Maozai & Zhu, Kai, 2013. "Variable selection in high-dimensional partially linear additive models for composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 56-67.
    3. Manuel Febrero-Bande & Wenceslao González-Manteiga & Manuel Oviedo de la Fuente, 2019. "Variable selection in functional additive regression models," Computational Statistics, Springer, vol. 34(2), pages 469-487, June.

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