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Research Based on High-Dimensional Fused Lasso Partially Linear Model

Author

Listed:
  • Aifen Feng

    (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)

  • Zhengfen Jin

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

  • Mengmeng Zhao

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

  • Xiaogai Chang

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

Abstract

In this paper, a partially linear model based on the fused lasso method is proposed to solve the problem of high correlation between adjacent variables, and then the idea of the two-stage estimation method is used to study the solution of this model. Firstly, the non-parametric part of the partially linear model is estimated using the kernel function method and transforming the semiparametric model into a parametric model. Secondly, the fused lasso regularization term is introduced into the model to construct the least squares parameter estimation based on the fused lasso penalty. Then, due to the non-smooth terms of the model, the subproblems may not have closed-form solutions, so the linearized alternating direction multiplier method (LADMM) is used to solve the model, and the convergence of the algorithm and the asymptotic properties of the model are analyzed. Finally, the applicability of this model was demonstrated through two types of simulation data and practical problems in predicting worker wages.

Suggested Citation

  • Aifen Feng & Jingya Fan & Zhengfen Jin & Mengmeng Zhao & Xiaogai Chang, 2023. "Research Based on High-Dimensional Fused Lasso Partially Linear Model," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2726-:d:1172279
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    References listed on IDEAS

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    4. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
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