Post-stratified Probability-Proportional-to-Size Sampling from Stratified Populations

Abstract

This paper develops statistical inference based on a post-stratified probability-proportional-to-size (pp) sample from a finite population. A pp sample selects the sample units with selection probabilities proportional to their size and measures them for the characteristic of interest. For each measured unit, the pp sample further creates position information (rank) in a comparison set of size M. The sample is then post-stratified into ranking classes based on their position information in the comparison set. A pp sample is expanded to stratified populations by selecting a pp sample from each stratum population to form the stratified pp sample. Using this stratified pp sample, we construct unbiased and Rao–Blackwell estimators for the mean of the stratified populations. Different sample size allocation procedures for stratum sample sizes are investigated. The new sampling design is applied to apple production data to estimate the total apple production in Turkey. Supplementary materials accompanying this paper appear online.