Conditions are given for admissibility of procedures invariant under two-dimensional translation. These conditions may be applied to obtain admissibility of (i) the best invariant procedure for estimating a two-dimensional location parameter and (ii) procedures which are Bayes in the class of procedures invariant under two-dimensional translation, the prior distribution being over values of some other parameter.
"Admissibility of Procedures in Two-Dimensional Location Parameter Problems." Ann. Statist. 2 (2) 248 - 266, March, 1974. https://doi.org/10.1214/aos/1176342661