Relaxing the Gaussian assumption in Shrinkage and SURE in high dimension

Understand

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.