It was pointed out in Chapter 2, Section 2.2, that if no a priori knowledge is specified concerning β, the criterion of minimization of a matrix-valued mean-square error is ill-posed. Nevertheless, there are some cases in which the choice of a particular scalar-valued definition of mean-square error makes it possible to obtain estimators with lower mean-square error than the Gauss–Markov estimator, for all β. In such cases, the Gauss–Markov estimator is “inadmissible” in the sense of Wald (1950). A situation of this kind was first discovered by Stein (1956).