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Statistical inference for population quantiles and variance in judgment post-stratified samples

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  • Ozturk, Omer

Abstract

A judgment post-stratified (JPS) sample is used in order to develop statistical inference for population quantiles and variance. For the pth order of the population quantile, a test is constructed, an estimator is developed, and a distribution-free confidence interval is provided. An unbiased estimator for the population variance is also derived. For finite sample sizes, it is shown that the proposed inferential procedures for quantiles are more efficient than corresponding simple random sampling (SRS) procedures, but less efficient than corresponding ranked set sampling (RSS) procedures. The variance estimator is less efficient, as efficient as, or more efficient than a simple random sample variance estimator for small, moderately small, and large sample sizes, respectively. Furthermore, it is shown that JPS sample quantile estimators and tests are asymptotically equivalent to RSS estimators and tests in their efficiency comparison.

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  • 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.
    • Handle: RePEc:eee:csdana:v:77:y:2014:i:c:p:188-205
    DOI: 10.1016/j.csda.2014.02.021
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188, May.
    7. 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.
    8. 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.
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    Cited by:

    1. Mozhgan Alirezaei Dizicheh & Nasrollah Iranpanah & Ehsan Zamanzade, 2021. "Bootstrap Methods for Judgment Post Stratification," Statistical Papers, Springer, vol. 62(5), pages 2453-2471, October.
    2. Ehsan Zamanzade & Michael Vock, 2018. "Some nonparametric tests of perfect judgment ranking for judgment post stratification," Statistical Papers, Springer, vol. 59(3), pages 1085-1100, September.
    3. 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.
    4. Amirhossein Alvandi & Armin Hatefi, 2023. "Analysis of Ordinal Populations from Judgment Post-Stratification," Stats, MDPI, vol. 6(3), pages 1-27, August.
    5. 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.
    6. 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.
    7. Zamanzade, Ehsan & Wang, Xinlei, 2017. "Estimation of population proportion for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 257-269.
    8. Omer Ozturk & Olena Kravchuk, 2021. "Judgment Post-stratified Assessment Combining Ranking Information from Multiple Sources, with a Field Phenotyping Example," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 329-348, September.
    9. Ali Dastbaravarde & Ehsan Zamanzade, 2020. "On estimation of $$P\left( X > Y \right) $$PX>Y based on judgement post stratification," Statistical Papers, Springer, vol. 61(2), pages 767-785, April.

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