Optimum Utilization of Auxiliary Information:πPsSampling of Two Units from a Stratum

Abstract

For the estimation of the population total of a charactery, defined over a finite population of known size, “optimum” sampling strategies for the case when auxiliary informationXof a type commonly met with in practice are recalled. A method of sampling two units from a stratum such that the probability of inclusion of one unit is exactly proportional to the value ofXon the unit is given. This method incidentally furnishes not only an optimum estimator of the population total but also a stable non-negative unbiased estimator of the variance of the main estimator. The method is compared with two other methods in varying probability sampling. Illustrative examples are given.