异方差一致协方差阵的估计方法研究  

Research on Estimation Method of Heteroscedasticity Consistent Covariance Matrix

作　　者：李顺勇[1] 李佳欣 LI Shunyong;LI Jiaxin(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,太原030006

出　　处：《河南科学》2023年第5期625-634,共10页Henan Science

基　　金：国家自然科学基金项目(82274360,61976128);2022年度山西省研究生教育教学改革课题(2022YJJG010);山西省高等学校教学改革创新项目(J2021059)。

摘　　要：处理回归模型中的异方差问题尤为重要的一点是对随机误差项的方差进行估计.考虑到非参数核估计和稳健估计在异方差构成未知的情况下在估计效果上仍具有一定优越性,因而将非参数N-W估计和两种稳健估计方法分别与估计加权最小二乘估计法相结合,先得出随机误差项方差的估计量,进而将其作为权矩阵对模型参数进行估计,并基于估计加权最小二乘法,对已有的加权异方差一致协方差估计方法进行扩展,提出了两个新的加权估计量WHC4m和WHC5m.通过实验可以发现,各估计方法在模型参数的估计和检验效果上差别较大,并且新提出的加权估计量比原有的异方差一致协方差估计量HC4m和HC5m在检验效果上表现更好.It is particularly important to estimate the variance of the random error term when dealing with heteroscedasticity in regression model.Considering that non-parametric kernel estimation and robust estimation still have certain superiority in estimation effect when heteroscedasticity composition is unknown,non-parametric N-W estimation and two robust estimation methods are combined with estimator weighted least square method respectively.Firstly,the estimator of variance of random error term is obtained,and then it is used as weight matrix to estimate model parameters.Based on the estimation weighted least square method,the existing weighted heteroscedasticity consistent covariance estimation method is extended,and two new weighted estimators,WHC4m and WHC5m,are proposed.Through the experiment,it can be found that the estimation methods differ greatly in the estimation and testing effect of model parameters,and the new weighted estimator is better than the original heteroscedasticity consistent covariance estimators HC4m and HC5m in the testing effect.

关 键 词：异方差 非参数核估计 加权异方差一致协方差估计 稳健估计 估计加权最小二乘法 

分 类 号：O212[理学—概率论与数理统计]