Gamma minimax robustness of bayes rules

Bayes rules are shown to be robust in multiple decision problems in the sense that they retain an optimality property, T-minimaxity, when the original distributions are replaced by families of E-contaminated versions of themselves and the prior is replaced by a family of priors on these e-contaminations. Thus, the Bayes rule is robust against inaccurately specified parameter spaces and, hence, inaccurately specified priors. Bounds are obtained on the amount of contamination which can be present with the Bayes rule remaining T-minimax.