We consider the problem of the estimation of the total of a stratified finite population. For two levels of prior knowledge about the stratification, we provide Bayes and pseudo-Bayes estimators that make use of this prior knowledge in sensible ways. We then note that admissibility results can be established for these estimators using the techniques of Meeden and Ghosh (1982, 1983) and indicate some possible natural extensions of the present work.
"Admissible Estimators for the Total of a Stratified Population that Employ Prior Information." Ann. Statist. 12 (2) 675 - 684, June, 1984. https://doi.org/10.1214/aos/1176346514