部分线性变系数模型的新复合分位数回归估计  

A Novel Composite Quantile Regression Estimation for the Partial Linear Variable Coefficient Models

作　　者：刘艳霞 芮荣祥 田茂再[1,2,3] LIU YANXIA;RUI RONGXIANG;TIAN MAOZAI(Center for Applied Statistics,School of Statistics,Renmin University of China,Beijing 100872,Chino;School of Statistics and Information,Xinjiang University of Finance and Economics,Xinjiang 830012,China;School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020,China)

机构地区：[1]中国人民大学应用统计科学研究中心,中国人民大学统计学院,北京100872 [2]新疆财经大学统计与信息学院,乌鲁木齐830012 [3]兰州财经大学统计学院,兰州730020

出　　处：《应用数学学报》2021年第2期159-174,共16页Acta Mathematicae Applicatae Sinica

基　　金：中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)项目成果:大数据分析的稳健统计理论与应用研究(编号:18XNL012)。

摘　　要：针对部分线性变系数模型的参数估计问题,提出了一种新复合分位数回归估计方法.利用复合分位数回归法估计参数部分,局部非线性复合分位数回归法估计变系数函数部分,并在若干正则条件下,证明了常系数和变系数函数估计量具有较好的渐近正态性质.通过随机模拟和实例分析,验证了所提估计方法在有限样本下的良好表现,有效的证明了所提方法的优越性.Based on the parameter estimation problem of partial linear variable-coefficient models,a novel composite quantile regression estimation method is proposed.The parameter part is estimated by using the composite quantile regression method,the variable coefficient function part is estimated by the local nonlinear composite quantile regression method.And under some regular conditions,it is proved that the estimators of constant coefficient and variable coefficient functions have better asymptotic normal properties.Through stochastic simulation and a real data analysis,the good performance of the proposed estimation method under limited samples is verified,which effectively proves the superiority of the proposed method.

关 键 词：部分线性变系数模型 复合分位数回归 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]