In a standard linear model, we explore the optimality of the least squares estimator under assuptions stronger than those for the Gauss-Markov theorem. The conclusion is then much stronger than that of the Gauss-Markov theorem. Specifically, two results are cited below: Under the assumption that the unobserved error [var epsilon] has a spherically symmetric distribution, the least squares estimator for the regression coefficient [beta] is shown to maximize the probability that [beta] - [beta] stays in any symmetric convex set among linear unbiased estimators [beta]. With the additional assumption that [var epsilon] is unimodal, the conclusion holds among equivariant estimators. The import of these results for risk functions is also discussed.
