On Extensions of the Gauss‐Markov Theorem to the Case of Stochastic Regression Coefficients
On Extensions of the Gauss‐Markov Theorem to the Case of Stochastic Regression Coefficients
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DOI：
10.1111/j.2517-6161.1984.tb01287.x
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发表时间：
1984-09
期刊：
影响因子：
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通讯作者：
D. Pfeffermann
中科院分区：
文献类型：
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作者：
D. Pfeffermann
文献中提出了将高斯-马尔可夫定理扩展到系数随机向量情况的几个定理。其中一些定理虽然表述和证明不同，但基于相同的假设并得出相似的结果。有些定理是文献中已经存在的定理的特例。在其他情况下，定理的基本假设和结论看似相似，但其差异并不明显。考虑了一种新的扩展，即未观察到的关系系数的最优预测。
Several theorems which extend the Gauss‐Markov theorem to the case of stochastic vectors of coefficients are presented in the literature. Some of these theorems, although differently formulated and proved, are based on the same assumptions and arrive at similar results. Some theorems are special cases of theorems, already existing in the literature. In other cases, theorems, which appear to be similar in their underlying assumptions and conclusions, differ in ways that are not immediately apparent. A new extension, optimal prediction of coefficients of unobserved relations, is considered.