Abstract
Abstract This paper investigates generalized Stein estimation under spherically symmetric distributions. We reconsider important results on possible improvements over the best invariant estimator by shrinkage estimators through a successful analytic technique via a global optimization problem. Specifically, minimaxity of the James–Stein estimators for p-variate shift models with p⩾4 and general spherically symmetric distributions is instructively demonstrated. In addition, we derive a robustness result for the (formal) Bayes estimators of Stein (Ann. Statist. 9 (1981)) by showing that they continue to be minimax for certain non-normal distributions.
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