"On Improved Shrinkage Estimators for Concave Loss"

Kubokawa, Tatsuya, Éric Marchand and William E. Strawderman

We consider minimax shrinkage estimation of a location vector of a spherically symmetric distribution under a loss function which is a concave function of the usual squared error loss. In particular for distributions which are scale mixtures of normals (and somewhat more generally), and for concave loss functions whose derivatives are completely monotone (and somewhat more generally), we give classes of minimax shrinkage estimators where the shrinkage constants are larger than those currently in the literature.