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Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model

Author

Listed:
  • Aifen Feng

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
    These authors contributed equally to this work.)

  • Xiaogai Chang

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
    These authors contributed equally to this work.)

  • Youlin Shang

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Jingya Fan

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

Abstract

This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrained least squares estimation is investigated, and the alternating-direction multiplier method (ADMM) is used to solve the model. The convergence is proved under certain conditions. Finally, numerical simulations are performed and applied to workers’ wage data from CPS85. The results show that the ADMM algorithm is very effective in solving high-dimensional partially linear models.

Suggested Citation

  • Aifen Feng & Xiaogai Chang & Youlin Shang & Jingya Fan, 2022. "Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model," Mathematics, MDPI, vol. 10(24), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4767-:d:1004252
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    References listed on IDEAS

    as
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    3. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    4. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    5. Ni, Xiao & Zhang, Hao Helen & Zhang, Daowen, 2009. "Automatic model selection for partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2100-2111, October.
    6. Hong-Xia Xu & Zhen-Long Chen & Jiang-Feng Wang & Guo-Liang Fan, 2019. "Quantile regression and variable selection for partially linear model with randomly truncated data," Statistical Papers, Springer, vol. 60(4), pages 1137-1160, August.
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    Citations

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    Cited by:

    1. Aifen Feng & Xiaogai Chang & Jingya Fan & Zhengfen Jin, 2023. "Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model," Mathematics, MDPI, vol. 11(19), pages 1-14, October.

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