控制单个随机解释变量条件下被解释变量平均改变量的估计方法

Average Change Estimation of the Explained Variable in Condition of Controlling Single Random Explanatory Variable

文章在将两个相关随机变量中的一个适当分解为两个随机变量的基础上,对解释变量完全是随机变量的不完全多重共线问题,给出了用一个原解释变量以及与其不相关随机解释变量线性表示被解释变量的表示方法。进而研究了单独控制一个原解释变量改变一个单位条件下被解释变量的平均改变量(单控改变量),给出了估计单控改变量的方法——剔除相关变量法,证明了估计量的无偏性和一致性,并证明了估计量方差依概率收敛到有效估计量的方差。

On the basis that one of the two correlated random variables is properly decomposed into two random variables, aiming at the problem that explanatory variables are totally the less-than perfect multi-collinearity of random variables, this paper presents a method to express the explained variable by an original explanatory variable and random explanatory variable linearity irrelevant with it, and studies the average change of the explained variable when one of the original explanatory variables is controlled to change a unit. The paper also gives a method to estimate the single control change, namely the dropping-a-correlated-variable method, and proves the unbiasedness, consistency of the estimator, and also proves that estimator variance depending on probability converges to the variance of the efficient estimator.