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

Omer Ozturk ()
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Omer Ozturk: Department of Statistics

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 4, No 9, 1113-1143

Abstract: Abstract 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 $$M > n$$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 show that Rao–Blackwell estimators outperform the same estimators constructed from a systematic sample.

Keywords: Systematic sample; Post-stratified sample; Judgment post-stratified sample; Rao–Blackwell estimator; Cluster sample; Ranked set sample; 62D05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11749-018-0618-y

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