On limits of uniquely best linear estimators

In a general linear model, it is shown that all admissible linear estimators are limits of linear estimators that are uniquely best at some point in an extended parameter set. The principal result shows that a linear estimator that is uniquely best at a point W2 among the multiple linear estimators that are best at a point W1 is the limit of uniquely best estimators at points approaching W1 along the line joining W1 and W2.