Optimum Utilization of Auxiliary Information: πPs Sampling of Two Units from a Stratum

Summary For the estimation of the population total of a character y, defined over a finite population of known size, “optimum” sampling strategies for the case when auxiliary information X of 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 of X on 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.