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

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  • Omer Ozturk

    (The Ohio State University)

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.

Suggested Citation

  • Omer Ozturk, 2019. "Post-stratified Probability-Proportional-to-Size Sampling from Stratified Populations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 693-718, December.
    • Handle: RePEc:spr:jagbes:v:24:y:2019:i:4:d:10.1007_s13253-019-00370-6
    DOI: 10.1007/s13253-019-00370-6
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    References listed on IDEAS

    as
    1. M. Al-Saleh & H. Samawi, 2007. "A note on inclusion probability in ranked set sampling and some of its variations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 198-209, May.
    2. Omer Ozturk, 2016. "Estimation of a Finite Population Mean and Total Using Population Ranks of Sample Units," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 181-202, March.
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    4. Ozturk, Omer & Jafari Jozani, Mohammad, 2014. "Inclusion probabilities in partially rank ordered set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 122-132.
    5. 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.
    6. 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.
    7. 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.
    8. Ali Dastbaravarde & Nasser Reza Arghami & Majid Sarmad, 2016. "Some theoretical results concerning non parametric estimation by using a judgment poststratification sample," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2181-2203, April.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
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    Cited by:

    1. M. Mahdizadeh & Ehsan Zamanzade, 2020. "Estimating asymptotic variance of M-estimators in ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1785-1803, December.

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