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A new ranked set sample estimator of variance

Author

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  • Steven N. MacEachern
  • Ömer Öztürk
  • Douglas A. Wolfe
  • Gregory V. Stark

Abstract

Summary. We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:2:p:177-188
    DOI: 10.1111/1467-9868.00331
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    References listed on IDEAS

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    1. Sinha Bimal K. & Sinha Bikas K. & Purkayastha Sumitra, 1996. "On Some Aspects Of Ranked Set Sampling For Estimation Of Normal And Exponential Parameters," Statistics & Risk Modeling, De Gruyter, vol. 14(3), pages 223-240, March.
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    Citations

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    Cited by:

    1. 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.
    2. Wang, You-Gan & Zhu, Min, 2005. "Optimal sign tests for data from ranked set samples," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 13-22, April.
    3. Elham Zamanzade & Majid Asadi & Afshin Parvardeh & Ehsan Zamanzade, 2023. "A ranked-based estimator of the mean past lifetime with an application," Statistical Papers, Springer, vol. 64(1), pages 161-177, February.
    4. 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.
    5. Zamanzade, Elham & Parvardeh, Afshin & Asadi, Majid, 2019. "Estimation of mean residual life based on ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 35-55.
    6. Ehsan Zamanzade, 2019. "EDF-based tests of exponentiality in pair ranked set sampling," Statistical Papers, Springer, vol. 60(6), pages 2141-2159, December.
    7. 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.
    8. Cesar Augusto Taconeli & Suely Ruiz Giolo, 2020. "Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data," Computational Statistics, Springer, vol. 35(4), pages 1827-1851, December.
    9. 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.
    10. Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    11. Ahmed N Albatineh & B.M. Golam Kibria & Meredith L Wilcox & Bashar Zogheib, 2014. "Confidence interval estimation for the population coefficient of variation using ranked set sampling: a simulation study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 733-751, April.
    12. Zamanzade, Ehsan & Wang, Xinlei, 2017. "Estimation of population proportion for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 257-269.
    13. Omer Ozturk & Steven MacEachern, 2004. "Order restricted randomized designs for control versus treatment comparison," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 701-720, December.
    14. 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.
    15. 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.
    16. Nader Gemayel & Elizabeth Stasny & James Tackett & Douglas Wolfe, 2012. "Ranked set sampling: an auditing application," Review of Quantitative Finance and Accounting, Springer, vol. 39(4), pages 413-422, November.
    17. M. Mahdizadeh & Ehsan Zamanzade, 2018. "Interval estimation of $$P(X," Computational Statistics, Springer, vol. 33(3), pages 1325-1348, September.
    18. M. Mahdizadeh & Ehsan Zamanzade, 2022. "New insights on goodness-of-fit tests for ranked set samples," Statistical Papers, Springer, vol. 63(6), pages 1777-1799, December.
    19. Zamanzade, Ehsan & Mahdizadeh, M., 2017. "A more efficient proportion estimator in ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 28-33.
    20. 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.
    21. Jesse Frey & Timothy G. Feeman, 2017. "Efficiency comparisons for partially rank-ordered set sampling," Statistical Papers, Springer, vol. 58(4), pages 1149-1163, December.
    22. 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.

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