一种改进的基于正交表的异方差估计方法  

An improved estimation method of the variance with orthogonal table based on adaptive estimation

作　　者：郭雅静 张晓琴 GUO Yajing;ZHANG Xiaoqin(School of Sciences,Hebei University of Architecture,Zhangjiakou,Hebei 075024,China;School of Statistics,Shanxi University of Finance and Economics,Taiyuan,Shanxi 030006,China)

机构地区：[1]河北建筑工程学院数理系,河北张家口075024 [2]山西财经大学统计学院,山西太原030006

出　　处：《贵州师范大学学报（自然科学版）》2022年第5期117-124,共8页Journal of Guizhou Normal University：Natural Sciences

基　　金：河北省省属高等学校基本科研业务费研究项目(2021QNJS11);河北建筑工程学院学术团队创新提升项目(数学与应用数学);山西省基础研究计划项目(201901D111320);山西省研究生教改项目(2019JG023);山西省留学回国人员科技活动择优资助项目(2019)。

摘　　要：线性回归模型中通常假设误差项具有相同的方差,然而在实际应用中,却不能保证这一假设成立,即误差项具有异方差性。这将使得利用普通最小二乘法得到的参数估计不是有效估计,此时无法对模型的参数进行显著性检验,预测精度也会降低,因此,对于异方差模型的处理以及误差项方差的估计是很有意义的。近年来提出的正交表方法给出了误差项协方差阵一个较好的估计。针对这一方法进行了改进,在已有的正交表方法中引入非参数估计,即在异方差形式未知的情况下,先利用正交表扩展模型,再用非参数的方法对各项方差给出估计。模拟结果与实例研究表明,提出的方法对误差项协方差阵的估计比原有的估计方法更加准确。In the linear regression model,the variance of the random error terms are usually assumed equal.But in practical application,we cannot guarantee this hypothesis,we call it heteroscedasticity.This will make the parameter estimation obtained by the ordinary least squares method is not an effective estimation.At this time,it is impossible to test the significance of the model parameters,and the prediction accuracy will also be reduced.Therefore,the study of heteroscedasticity model is very necessary,which leads to the estimation of the variance of the random error terms.The orthogonal table method proposed gives a better estimation of the covariance matrix of the random error terms in recent years.This paper improved the method of parameter estimation and nonparametric estimation is introduced into the existing orthogonal table method,that is,when the form of heteroscedasticity is unknown,we use the orthogonal table to extend the model,and then estimate the variance by the non parametric method.Simulation results and case studies show that the method proposed in this paper is more accurate than the original method for the covariance matrix estimation.

关 键 词：异方差 正交表 HCCMES 协方差阵 

分 类 号：F272[经济管理—企业管理] O212[经济管理—国民经济]