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

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.