变系数模型的局部组合分位数估计  

Local composite quantile regression for the varying coefficient model

作　　者：解其昌[1] 

机构地区：[1]山东工商学院经济学院,山东烟台264005

出　　处：《浙江大学学报（理学版）》2015年第3期286-292,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家社科基金资助项目(14BJY180);山东省自然科学基金资助项目(ZR2014GQ009)

摘　　要：变系数模型推广了经典的线性模型,能灵活描绘变量间的非线性和交互性特征.考虑跨越一系列分位点的变系数模型的稳健估计,采用局部组合分位数回归方法,给出了该模型估计的局部Bahadur表示和渐近正态分布性质.证明了所得的估计量能够满足非参数收敛率要求.同时,模型计算容易执行且不需要指定误差分布的具体形式.进而推导了最优窗宽的表达式并提供了一个基于分位数交叉核实准则的窗宽选择方法.通过Monte Carlo模拟,检验了局部组合分位数估计变系数模型的有限样本性质.The varying coefficient model is a useful generalization of classical linear models. It offers a flexible ap- proach to modeling the nonlinearity and interactions between the covariates. This paper considers the robust estima- tion crossing a series of quantiles for the varying coefficient model. By employing the local composite quantile regres- sion, we have derived the local Bahadur representation of the varying coefficient model and obtained the asymptotic normality of the resulting estimator. Furthermore, the estimator of the varying coefficient model can achieve the nonparametric convergence rate. The estimation procedure is easy to implement and requires no specification of the error distribution. In addition, the expression of the optimal bandwidth is given, and a bandwidth selector based on the quantile regression of the cross validation criterion is proposed. Monte Carlo simulation is conducted to examine the finite sample performance of the proposed method.

关 键 词：变系数模型 分位数回归 局部多项式 渐近正态分布 MONTE CARLO模拟 

分 类 号：O212[理学—概率论与数理统计]