A study of the performance of an alternative estimator of population total for unequal probability sampling procedures

This paper describes an empirical study of the performance of the estimator suggested by Stuart. The Stuart’s estimator of population total is a modified Horvitz-Thompson estimator for unequal probability sampling without replacement which uses transformed values of the variable under study. The transformation is a simple location-shift. Although the Stuart’s estimator is more precise than the Horvitz-Thompson estimator when the optimal location-shift is known, the study shows that actually a loss in precision can occur when the estimated location-shift deviates from the unknown optimal value.