Minimum Variance Estimation in Stratified Sampling

Abstract

Abstract This article discusses efficiency properties of some common stratified estimators, in the context of a superpopulation model, relative to the greatest lower bound on the variance of the Horvitz—Thompson estimator. The estimators discussed use both Dalenius—Hodges and model-based survey sampling (MBSS) stratification and a variety of sample allocation methods, including optimum, proportionate, and uniform sample allocation. The main result is that both Dalenius—Hodges stratification with optimal allocation and MBSS stratification with uniform allocation yield approximately minimum variance estimators, with convergence to the lower bound at rate O(L –2), where L is the number of strata. Since this lower bound has been shown to hold for many types of finite population estimators, the results derived here have broad implications. A series of examples is presented in which Dalenius—Hodges/optimum allocation is consistently more efficient than MBSS/uniform allocation.