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Automatic structure recovery for additive models

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  • Yichao Wu
  • Leonard A. Stefanski

Abstract

We propose an automatic structure recovery method for additive models, based on a backfitting algorithm coupled with local polynomial smoothing, in conjunction with a new kernel-based variable selection strategy. Our method produces estimates of the set of noise predictors, the sets of predictors that contribute polynomially at different degrees up to a specified degree M, and the set of predictors that contribute beyond polynomially of degree M. We prove consistency of the proposed method, and describe an extension to partially linear models. Finite-sample performance of the method is illustrated via Monte Carlo studies and a real-data example.

Suggested Citation

  • Yichao Wu & Leonard A. Stefanski, 2015. "Automatic structure recovery for additive models," Biometrika, Biometrika Trust, vol. 102(2), pages 381-395.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:2:p:381-395.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu070
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    References listed on IDEAS

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    1. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
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    Cited by:

    1. Hang Yu & Yuanjia Wang & Donglin Zeng, 2023. "A general framework of nonparametric feature selection in high‐dimensional data," Biometrics, The International Biometric Society, vol. 79(2), pages 951-963, June.
    2. Doksum, Kjell A. & Jiang, Jiancheng & Sun, Bo & Wang, Shuzhen, 2017. "Nearest neighbor estimates of regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 64-74.
    3. Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    4. Li Liu & Hao Wang & Yanyan Liu & Jian Huang, 2021. "Model pursuit and variable selection in the additive accelerated failure time model," Statistical Papers, Springer, vol. 62(6), pages 2627-2659, December.
    5. Xin He & Junhui Wang, 2020. "Discovering model structure for partially linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 45-63, February.

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