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Variance estimation using judgment post-stratification

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  • Jesse Frey
  • Timothy Feeman

Abstract

We consider the problem of estimating the variance of a population using judgment post-stratification. By conditioning on the observed vector of ordered in-stratum sample sizes, we develop a conditionally unbiased nonparametric estimator that outperforms the sample variance except when the rankings are very poor. This estimator also outperforms the standard unbiased nonparametric variance estimator from unbalanced ranked-set sampling. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:3:p:551-569
    DOI: 10.1007/s10463-012-0386-5
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    References listed on IDEAS

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    1. Juan Du & Steven N. MacEachern, 2008. "Judgement Post-Stratification for Designed Experiments," Biometrics, The International Biometric Society, vol. 64(2), pages 345-354, June.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. McIntyre, G.A., 2005. "A Method for Unbiased Selective Sampling, Using Ranked Sets," The American Statistician, American Statistical Association, vol. 59, pages 230-232, 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. 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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    Citations

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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. Zamanzade, Ehsan & Vock, Michael, 2015. "Variance estimation in ranked set sampling using a concomitant variable," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 1-5.
    4. 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.
    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. 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. Zamanzade, Ehsan & Wang, Xinlei, 2017. "Estimation of population proportion for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 257-269.
    9. 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.
    10. 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.
    11. 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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