Abstract
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, $\theta$, cannot be improved on near $\infty$ at order $\|\theta\|^{-2}$.
Citation
Lawrence D. Brown. "A Necessary Condition for Admissibility." Ann. Statist. 8 (3) 540 - 544, May, 1980. https://doi.org/10.1214/aos/1176345007
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