Edgar Bueno: A comparison of stratified simple random sampling and probability proportional-to-size sampling

Abstract: The sampling strategy that couples probability proportional-to-size sampling with the GREG estimator has sometimes been called “optimal”, as it minimizes the anticipated variance. This optimality, however, relies on the assumption that the finite population of interest can be seen as a realization of a superpopulation model that is known to the statistician. Making use of the same model, the strategy that couples model-based stratification with the GREG estimator is an alternative that, although theoretically less efficient, has shown to be sometimes more efficient than the so-called optimal strategy from an empirical point of view. We compare the two strategies from both analytical and simulation standpoints and show that optimality is not robust towards misspecifications of the model. In fact gross errors may be observed when a misspecified model is used.