ABSTRACTLet t1,…,tk be independent unbiased estimators of a parameter τ. Let t* = Σαiti have minimum variance among unbiased linear estimators of τ, and let , be any linear combinations with () independent of t1,…,tk. We prove that is unbiased for τ and that the ratio of the variance of to the variance of t* is where is the mean square error of as an estimator of αi.