异方差模型中协方差阵的估计研究  

Research on covariance matrix estimation in heteroscedasticity model

作　　者：李顺勇[1] 郭雅静 张晓琴[1] LI Shunyong;GUO Yajing;ZHANG Xiaoqin(School of Mathematical Sciences,Shanxi University,Taiyuan,Shanxi 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《贵州师范大学学报（自然科学版）》2019年第1期69-77,共9页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金(61573229);山西省基础研究计划项目(201701D121004);山西省回国留学人员科研资助项目(2017-020);山西省高等学校教学改革创新项目(J2017002)

摘　　要：在异方差模型中,尽管回归系数的普通最小二乘(OLS)估计仍能保持无偏性,但其对应的协方差阵估计不再一致。解决异方差问题,对随机误差项协方差阵的估计显得尤为重要。基于异方差形式未知的情况下,非参数估计的良好效果,应用不同的非参数方法对误差项的协方差阵给出估计,进而通过估计加权最小二乘法得到回归系数的估计,并在已有的加权异方差一致协方差阵估计的基础上进行了拓展。模拟实验和实例分析表明,不同的非参数方法在回归系数的估计和模型的检验方面效果都有很大的差异。In the heteroscedasticity model,although the ordinary least squares(OLS)estimator of the regression coefficient can still remain unbiased,its corresponding covariance matrix estimator is no longer consistent.To solve the heteroskedastic problem,it is especially important to estimate the covariance matrix of random error terms.Based on the excellent effect of the non-parametric estimation when the form of heteroscedasticity is unknown,different non-parametric methods are used to estimate the covariance matrix of the error terms and then the regression coefficient is estimated by the estimated weighted least squares method.Some weighted heteroskedasticity consistent covariance matrix estimations are extended on the basis of it.Simulation experiments and a case study show that different nonparametric methods have great differences in the estimation of regression coefficients and the effects of model test.

关 键 词：异方差 非参数方法 加权最小二乘法 加权异方差一致协方差阵估计 

分 类 号：O21[理学—概率论与数理统计]