Sampling Design for Reducing the Variance Under the Population Model

Much research carried out on piPS sampling schemes seems to have focused on the operational features for simpler selection algorithm than on their capacity to yield a small variance for an estimator. Accordingly, the user is left to accept whatever sampling design emerges from the used scheme. We suggest an alterntive method to implement a sampling design to reduce the variance of the Horvitz and Thompson (1952) estimator, if the population model involving an auxiliary variable is available at the design stage. This method draws its inspiration from the one of Raj(1956). With respect to the joint probabilities, the method is compared with Sampford(1967) s method, which is one of the popular piPS sampling schemes, using an illustrative example. The proposed method appears to be simple to use in practice and bring about reduction in variance.