On Estimating a Linear Combination of Strata Means with Random Sample Sizes

In finite sampling it is widely believed that the probability sampling distribution is irrelevant for inference from a given sample. A super-population model in stratified sampling is investigated to show that the probability sampling distribution is relevant. It is proved that the traditional estimator of a linear combination of strata means, which is admissible and minimax when the vector of sample sizes is fu;ed, is inadmissible when the vector of sample sizes is random. Two alternative estimators are investigated. Based on analysis which is partly analytical and partly numerical, it appears that both of them are better than the traditional estimator.