Collinearity and Optimal Restrictions on Regression Parameters for Estimating Responses
Collinearity and Optimal Restrictions on Regression Parameters for Estimating Responses
复制标题
用于估计响应的回归参数的共线性和最优限制
DOI：
10.1080/00401706.1981.10487652
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发表时间：
1981
期刊：
影响因子：
2.5
通讯作者：
Sung H. Park
中科院分区：
文献类型：
--
作者：
Sung H. Park
多元线性回归中自变量之间的共线性会严重影响自变量在某个感兴趣区域的响应估计精度。共线性被证明是这样一种情况，其中对回归参数β存在一些线性限制，这可能会产生比均方误差上下文中的普通最小二乘估计更好的响应估计。本文研究了约束条件，给出了均方误差意义下的最优约束条件。证明了在最优约束下β的最小二乘估计与β的主成分估计是一致的。
Collinearity among independent variables in multiple linear regression can have severe effects on the precision of response estimation for some region of interest of independent variables. Collinearity is shown to be a situation in which there exist some linear restrictions on the regression parameters, β, that might yield better response estimators than the ordinary least squares estimators in the mean squared error context. This paper studies restrictions and formulates optimal restrictions in the sense of mean squared error. It is shown that the least squares estimator of β under the optimal restrictions is identical to a principal component estimator of β.