If the errors of a linear model are normally distributed and if quadratic loss is used, it is known, that the Gauss-Markov-estimator   is the best unbiased estimator of an estimable function η. Under certain conditions this is also true for convex loss. It we know only, that the error distribution lies in a certain class of distributions, and the normal distribution is in this class too, then, it is shown, that   becomes minimax relative to this class.