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Parameter Estimation of the Partially Linear Quantile Regression Model Under Monotonic Constraints

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  • Shujin Wu
  • Zhilin Yu
  • Shanshan Liang
  • Yanke Ren

Abstract

The paper brings forward the partially linear quantile regression model by incorporating monotonic constraints, which are common in real‐world relationships between variables. It introduces two novel parameter estimation methods, that is, the coordinate descent method and the profile likelihood method, which eliminate the extensive tuning and simplify the estimation process. Theoretical analysis confirms the estimator’s consistency and a convergence rate of n−1/3. Numerical simulations and case studies demonstrate the superiority of these methods over traditional approaches, particularly in estimating the nonparametric components of the model, highlighting their potential for practical use in various fields.

Suggested Citation

  • Shujin Wu & Zhilin Yu & Shanshan Liang & Yanke Ren, 2025. "Parameter Estimation of the Partially Linear Quantile Regression Model Under Monotonic Constraints," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:6421789
    DOI: 10.1155/jom/6421789
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    References listed on IDEAS

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    1. Hamilton, Scott A. & Truong, Young K., 1997. "Local Linear Estimation in Partly Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 1-19, January.
    2. Du, Jiang & Sun, Zhimeng & Xie, Tianfa, 2013. "M-estimation for the partially linear regression model under monotonic constraints," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1353-1363.
    3. Weihua Zhao & Riquan Zhang & Yazhao Lv & Jicai Liu, 2017. "Quantile regression and variable selection of single-index coefficient model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 761-789, August.
    4. de Leeuw, Jan & Hornik, Kurt & Mair, Patrick, 2009. "Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i05).
    5. Graciela Boente & Daniela Rodriguez & Pablo Vena, 2020. "Robust estimators in a generalized partly linear regression model under monotony constraints," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 50-89, March.
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