分位数回归下的动态单指标变系数模型

This paper studies a novel dynamic single index varying coefficient quantile regression model, which reflects the dynamic interaction between explanatory variables and the response variable, and covers many important models as special cases. In order to improve the interpretability and estimation accuracy, this paper further discusses the semi-varying structure of the model. Firstly, we use the B-spline method to obtain the estimators of the varying coefficient function and the index function. Secondly, the semi-varying model is identified based on the penalty function method. We also propose an estimation procedure for this semi-parametric model. In addition, We establish the consistency and asymptotic normality of each estimator, and both parametric and nonparametric estimators can achieve the optimal convergence rate. Numerical simulations show that the proposed models and estimation methods enjoy excellent properties. Finally, we analyze a NO₂ data set to demonstrate the performance of the proposed method in practical applications.