Conditional Properties of Some Estimators in Stratified Sampling

Abstract

Abstract The prediction properties of the stratified expansion estimator, the separate and combined ratio estimators, and the separate and combined regression estimators are studied under a model appropriate to a population stratified on a size variable. Several estimators of variance for each total estimator are considered, including standard ones from probability sampling theory, alternative choices derived from a superpopulation model, and the jackknife. The theory is tested in an empirical study using a real population. Earlier studies of the ratio and regression estimators under simple random sampling plans have illustrated that conditional properties of those estimators and of the linearization variance estimators that are often used with them can be much different and less desirable than unconditional properties. Whether similar results hold for stratified samples and estimators has been the subject of some debate. This article illustrates both theoretically and empirically that the use of stratifi...