A Necessary Condition for Admissibility

The main theorem of this note is required in a paper of Brown. Briefly, the theorem shows that procedures which can be improved on in a neighborhood of infinity are either inadmissible or are generalized Bayes for a (possibly improper) prior whose rate of growth at infinity is of an appropriate order. This theorem is applied here to show that the risk of the usual estimator of a two dimensional normal mean, θ, cannot be improved on near ∞ at order ∥θ∥−2