Relaxing the Gaussian assumption in shrinkage and SURE in high dimension Article Swipe
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1214/22-aos2208
· OA: W3015000206
Shrinkage estimation is a fundamental tool of modern statistics, pioneered by\nCharles Stein upon his discovery of the famous paradox involving the\nmultivariate Gaussian. A large portion of the subsequent literature only\nconsiders the efficiency of shrinkage, and that of an associated procedure\nknown as Stein's Unbiased Risk Estimate, or SURE, in the Gaussian setting of\nthat original work. We investigate what extensions to the domain of validity of\nshrinkage and SURE can be made away from the Gaussian through the use of tools\ndeveloped in the probabilistic area now known as Stein's method. We show that\nshrinkage is efficient away from the Gaussian under very mild conditions on the\ndistribution of the noise. SURE is also proved to be adaptive under similar\nassumptions, and in particular in a way that retains the classical asymptotics\nof Pinsker's theorem. Notably, shrinkage and SURE are shown to be efficient\nunder mild distributional assumptions, and particularly for general isotropic\nlog-concave measures.\n
