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Variable Selection for Additive Quantile Regression with Nonlinear Interaction Structures

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  • Yongxin Bai

    (School of Science, Beijing Information Science and Technology University, Beijing 100872, China)

  • Jiancheng Jiang

    (Department of Mathematics and Statistics & School of Data Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA)

  • Maozai Tian

    (Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100192, China)

Abstract

In high-dimensional data analysis, main effects and interaction effects often coexist, especially when complex nonlinear relationships are present. Effective variable selection is crucial for avoiding the curse of dimensionality and enhancing the predictive performance of a model. In this paper, we introduce a nonlinear interaction structure into the additive quantile regression model and propose an innovative penalization method. This method considers the complexity and smoothness of the additive model and incorporates heredity constraints on main effects and interaction effects through an improved regularization algorithm under marginality principle. We also establish the asymptotic properties of the penalized estimator and provide the corresponding excess risk. Our Monte Carlo simulations illustrate the proposed model and method, which are then applied to the analysis of Parkinson’s disease rating scores and further verify the effectiveness of a novel Parkinson’s disease (PD) treatment.

Suggested Citation

  • Yongxin Bai & Jiancheng Jiang & Maozai Tian, 2025. "Variable Selection for Additive Quantile Regression with Nonlinear Interaction Structures," Mathematics, MDPI, vol. 13(9), pages 1-28, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1522-:d:1649533
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    References listed on IDEAS

    as
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