Efficiency of Estimator of Probability Proportional to Size with and without Replacement

Abstract

Efficiency refer to how well a sampling method extracts info from a population relative to effort /cost and method is efficient if it gives precise estimate with a small sample. Estimator is efficient if it has a low variance. This research focused on the efficiency of probability proportional to size sampling scheme estimators. Probability proportional to size with replacement, Hansen-Hurwitz estimator and Probability proportional to size without replacement, Rao-Hartley-Cochran estimator were compared in terms of estimation and efficiency. The empirical comparison of the population total, minimum variance and relative efficiency were used in assessing the efficiency. Probability proportional to size with replacement, (Hansen-Hurwitz) estimator had the higher population total estimate for some years indicating that population total differed by year. Probability proportional to size sampling without replacement estimator, (Rao–Hartley–Cochran) estimator thus had a smaller variance, hence more efficient performed better than the conventional Hansen–Hurwitz estimator in terms of variance reduction.