SHRINKAGE ESTIMATORS WITH GENERAL QUADRATIC LOSS AND DIFFERENTIABLE OR PARTIALLY DIFFERENTIABLE SHRINKAGE FUNCTION

We place ourselves in the n-dimensional normal linear model, for which the variance is known up to a multiplicative factor. If y is observed, we denote by x the associated maximum likelihood estimator and z=y-x. We denote H(x,z) the realized shrinkage. One is dealing here with an unbiased estimator of the risk using either the differentiability with respect to x and z of H, or the partially differentiability of H with respect to x. © 1990, Taylor & Francis Group, LLC. All rights reserved.