  We consider the problem of estimating the error variance in a general linear
model when the error distribution is assumed to be spherically symmetric, but
not necessary Gaussian. In particular we study the case of a scale mixture of
Gaussians including the particularly important case of the multivariate-t
distribution. Under Stein's loss, we construct a class of estimators that
improve on the usual best unbiased (and best equivariant) estimator. Our class
has the interesting double robustness property of being simultaneously
generalized Bayes (for the same generalized prior) and minimax over the entire
class of scale mixture of Gaussian distributions.
