Admissible estimators for the total of a stratified population that employ prior information (Q1090023)

Consider a population containing N units, labeled 1,2,...,N, where y is the real variate of a characteristic attached to each unit, the problem is to estimate the population total T. Suppose this population to be stratified into strata 1,2,...,J. The authors propose two estimators, where one of them is considered under the situation where a priori beliefs about likely stratum memberships of all units are exchangeable, and the other is where they are not exchangeable. They prove that these estimators are admissible, using the techniques of the second author and \textit{M. Ghosh} [ibid. 11, 296-305 (1983; Zbl 0508.62012); see also ibid. 9, 846-852 (1981; Zbl 0472.62013)], and they also prove that the sampling strategies associated with these estimators are uniformly admissible.