Statistical inference using rank-based post-stratified samples in a finite population

In this paper, we consider statistical inference based on post-stratified samples from a finite population. We first select a simple random sample (SRS) of size n and identify their population ranks. Conditioning on these population ranks, we construct probability mass functions of the sample ranks of n units in a larger sample of size M > n. The n units in SRS are then post-stratified into d classes using conditional sample ranks. The sample ranks are constructed with two different conditional distributions leading to two different sampling designs. The first design uses a conditional distribution given n ordered population ranks. The second design uses a conditional distribution given a single (marginal) unordered population rank. The paper introduces unbiased estimators for the population mean, total, and their variances based on the post-stratified samples from these two designs. The conditional distributions of the sample ranks are used to construct Rao-Blackwell estimator for the population mean and total. We showthat Rao-Blackwell estimators outperform the same estimators constructed from a systematic sample.