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We consider quasi-admissibility/inadmissibility of Stein-type shrinkageestimators of the mean of a multivariate normal distribution with covariancematrix an unknown multiple of the identity. Quasi-admissibility/inadmissibilityis defined in terms of non-existence/existence of a solution to a differentialinequality based on Stein's unbiased risk estimate (SURE). We find a sharpboundary between quasi-admissible and quasi-inadmissible estimators related tothe optimal James-Stein estimator. We also find a class of priors related tothe Strawderman class in the known variance case where the boundary betweenquasi-admissibility and quasi-inadmissibility corresponds to the boundarybetween admissibility and inadmissibility in the known variance case.Additionally, we also briefly consider generalization to the case of generalspherically symmetric distributions with a residual vector.

A sharp boundary for SURE-based admissibility for the Normal means problem under unknown scale