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Comparison of the Stein and the usual estimators for the regression error variance under the Pitman nearness criterion when variables are omitted

机译:当变量被省略时,Pitman接近度准则下斯坦因估计量与常用估计量的回归误差方差的比较

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摘要

This paper compares the Stein and the usual estimators of the error variance under the Pitman nearness (PN) criterion in a regression model which is mis-specified due to missing relevant explanatory variables. The exact expression of the PN-probability is derived and numerically evaluated. Contrary to the well-known result under mean squared errors (MSE), with the PN criterion the Stein variance estimator is uniformly dominated by the usual estimator when no relevant variables are excluded from the model. With an increased degree of model mis-specification, neither estimator strictly dominates the other.
机译:本文比较了在Pitman接近度(PN)准则下,由于缺少相关的解释变量而被错误指定的Stein和Pitman接近度(PN)准则下误差方差的常用估计量。得出PN概率的精确表达式并进行数值评估。与均方误差(MSE)下的众所周知的结果相反,使用PN准则,当模型中没有任何相关变量时,斯坦因方差估算器由通常的估算器统一支配。随着模型错误指定程度的增加,两个估算器都不能严格支配另一个模型。

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