Optimality criteria in survey sampling

Abstract

This paper attempts to fill the gap between some different and conflicting approaches in survey sampling. Based on a fixed population regression-type model, a class of optimality criteria similar to those well accepted in optimal experimental design theory is introduced. The minimax and superpopulation approaches in survey sampling turn out to correspond to two extreme criteria in the proposed class. This helps understand the role of randomization. The strategy of simple random sampling with sample mean and the Rao-Hartley-Cochran strategy are shown to be criterion-robust.