  Shrinkage estimation is a fundamental tool of modern statistics, pioneered by
Charles Stein upon his discovery of the famous paradox involving the
multivariate Gaussian. A large portion of the subsequent literature only
considers the efficiency of shrinkage, and that of an associated procedure
known as Stein's Unbiased Risk Estimate, or SURE, in the Gaussian setting of
that original work. We investigate what extensions to the domain of validity of
shrinkage and SURE can be made away from the Gaussian through the use of tools
developed in the probabilistic area now known as Stein's method. We show that
shrinkage is efficient away from the Gaussian under very mild conditions on the
distribution of the noise. SURE is also proved to be adaptive under similar
assumptions, and in particular in a way that retains the classical asymptotics
of Pinsker's theorem. Notably, shrinkage and SURE are shown to be efficient
under mild distributional assumptions, and particularly for general isotropic
log-concave measures.
