分位数回归下的动态单指标变系数模型  

Quantile Regression of Dynamic Single Index Varying Coefficient Models

作　　者：管欣 尤进红 周勇[3] 徐国英 Xin GUAN;Jin Hong YOU;Yong ZHOU;Guo Ying XU(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,P.R.China;School of Statistics and Management,Shanghai University of Finance and Economics,Shanghai 200433,P.R.China;Shanghai Key Laboratory of Advanced Theory and Application in Statistics and Data Science,MOE,and Academy of Statistics and Interdisciplinary Sciences,East China Normal University,Shanghai 200062,P.R.China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]上海财经大学统计与管理学院,上海200433 [3]统计与数据科学前沿理论及应用教育部重点实验室,华东师范大学统计交叉科学研究院和统计学院,上海200062

出　　处：《数学学报（中文版）》2024年第1期45-71,共27页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11971291,71931004);国家重点研发计划资助项目(2021YFA1000100,2021YFA1000101);中南财经政法大学中央高校基本科研业务费专项资金资助项目(2722022BQ045)。

摘　　要：本文研究一类新颖的动态单指标变系数分位数回归模型,该模型反映了响应变量与解释变量之间的动态交互效应,并包含许多重要的模型为特例.为提高模型的可解释性和估计的精确度,讨论了模型的半变系数结构.首先,基于B样条方法得到变系数函数和指标函数的估计,采用惩罚函数方法识别模型的半变系数结构,提出了该半参数模型的估计方法.其次,建立了各估计量的相合性和渐近正态性,并且参数估计量和非参数估计量均可达到最优收敛速度.数值模拟表明本文所提出的模型和估计方法具有优良的性质.最后,分析一组NO2数据以展示所提方法在实际应用的表现.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.

关 键 词：动态交互效应 单指标变系数模型 半变系数模型 B样条 分位数回归 

分 类 号：O212.1[理学—概率论与数理统计]