再议普通最小二乘法下回归系数的性质

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。

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

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.