  We look at stochastic optimization problems through the lens of statistical
decision theory. In particular, we address admissibility, in the statistical
decision theory sense, of the natural sample average estimator for a stochastic
optimization problem (which is also known as the empirical risk minimization
(ERM) rule in learning literature). It is well known that for some simple
stochastic optimization problems, the sample average estimator may not be
admissible. This is known as {\em Stein's paradox} in the statistics
literature. We show in this paper that for optimizing stochastic linear
functions over compact sets, the sample average estimator is admissible.
Moreover, we study problems with convex quadratic objectives subject to box
constraints. Stein's paradox holds when there are no constraints and the
dimension of the problem is at least three. We show that in the presence of box
constraints, admissibility is recovered for dimensions 3 and 4.
