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B spline variable selection for the single index models

Author

Listed:
  • Jianbo Li

    (Guangzhou University
    Jiangsu Normal University)

  • Yuan Li

    (Guangzhou University)

  • Riquan Zhang

    (East China Normal University)

Abstract

Through the nonconcave penalized least squares method, we consider the variable selection in the full nonparametric regression models with the B spline-based single index approximation. Under some regular conditions, we show that the resulting estimates with SCAD and HARD thresholding penalties enjoy $$\sqrt{n}$$ n -consistency and oracle properties. We use some simulation studies and a real example to illustrate the performance of our proposed variable selection procedure.

Suggested Citation

  • Jianbo Li & Yuan Li & Riquan Zhang, 2017. "B spline variable selection for the single index models," Statistical Papers, Springer, vol. 58(3), pages 691-706, September.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0721-z
    DOI: 10.1007/s00362-015-0721-z
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    References listed on IDEAS

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    Cited by:

    1. Suli Cheng & Jianbao Chen, 2021. "Estimation of partially linear single-index spatial autoregressive model," Statistical Papers, Springer, vol. 62(1), pages 495-531, February.
    2. Huilan Liu & Hu Yang & Changgen Peng, 2019. "Weighted composite quantile regression for single index model with missing covariates at random," Computational Statistics, Springer, vol. 34(4), pages 1711-1740, December.
    3. Kangning Wang & Xiaofei Sun, 2020. "Efficient parameter estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data," Statistical Papers, Springer, vol. 61(3), pages 967-995, June.

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