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

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  • Omer Ozturk

    (Department of Statistics)

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.

Suggested Citation

  • Omer Ozturk, 2019. "Statistical inference using rank-based post-stratified samples in a finite population," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1113-1143, December.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:4:d:10.1007_s11749-018-0618-y
    DOI: 10.1007/s11749-018-0618-y
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    References listed on IDEAS

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    1. Omer Ozturk, 2017. "Statistical inference with empty strata in judgment post stratified samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1029-1057, October.
    2. Xinlei Wang & Johan Lim & Lynne Stokes, 2008. "A Nonparametric Mean Estimator for Judgment Poststratified Data," Biometrics, The International Biometric Society, vol. 64(2), pages 355-363, June.
    3. Wang, Xinlei & Stokes, Lynne & Lim, Johan & Chen, Min, 2006. "Concomitants of Multivariate Order Statistics With Application to Judgment Poststratification," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1693-1704, December.
    4. Ozturk, Omer, 2014. "Statistical inference for population quantiles and variance in judgment post-stratified samples," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 188-205.
    5. Jesse Frey, 2012. "Constrained nonparametric estimation of the mean and the CDF using ranked-set sampling with a covariate," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 439-456, April.
    6. Steven N. MacEachern & Elizabeth A. Stasny & Douglas A. Wolfe, 2004. "Judgement Post-Stratification with Imprecise Rankings," Biometrics, The International Biometric Society, vol. 60(1), pages 207-215, March.
    7. Jesse Frey & Omer Ozturk, 2011. "Constrained estimation using judgment post-stratification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 769-789, August.
    8. Frey, Jesse & Feeman, Timothy G., 2012. "An improved mean estimator for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 418-426.
    9. Jesse Frey & Timothy Feeman, 2013. "Variance estimation using judgment post-stratification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 551-569, June.
    10. Xinlei Wang & Ke Wang & Johan Lim, 2012. "Isotonized CDF Estimation from Judgment Poststratification Data with Empty Strata," Biometrics, The International Biometric Society, vol. 68(1), pages 194-202, March.
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