On Extensions of the Gauss-Markov Theorem to the Case of Stochastic Regression Coefficients

SUMMARY 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.