再议普通最小二乘法下回归系数的性质  

Further Discussion on Properties of Regression Coefficient Under Ordinary Least Square Method

作　　者：伍兴国[1] 雷钦礼[2] Wu Xingguo;Lei Qinli(Dongguan Polytechnic,Dongguan Guangdong 523808,China;College of Economics,Jinan University,Guangzhou 510632,China)

机构地区：[1]东莞职业技术学院,广东东莞523808 [2]暨南大学经济学院,广州510632

出　　处：《统计与决策》2020年第1期10-14,共5页Statistics & Decision

基　　金：东莞职业技术学院院级科研基金资助项目(政201811)

摘　　要：文章从个体的角度探讨最小二乘法下的估计系数的形成过程,得出一元回归中的回归系数是各个数据点上的回归系数以Epanechnikov核函数进行加权形式的。并在此基础上,推广到多元线性回归,多元线性回归的估计系数本质上为一种参数结构,它是以自变量的协方差矩阵为联系纽带,将回归系数分解为偏回归系数,将两个系数结合起来澄清目前计量经济学和统计学的一些问题。This paper discusses the formation process of the estimated coefficient under the least square method from the perspective of individuals,and concludes that the regression coefficient in unitary regression is the regression at each data point weighted by the Epanechnikov kernel function,and on this basis,it is generalized to multiple linear regression,whose estimated coefficient is essentially a parameter structure,which takes the covariance matrix of the independent variables as the link,decomposing the regression coefficient into partial regression coefficient,and combining the two coefficients to clarify some of the current problems in econometrics and statistics.

关 键 词：最小二乘法 协方差矩阵 偏回归系数 结构突变 效用 

分 类 号：F224.0[经济管理—国民经济]