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On estimation of $$P\left( X > Y \right) $$PX>Y based on judgement post stratification

Author

Listed:
  • Ali Dastbaravarde

    (Yazd University)

  • Ehsan Zamanzade

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

Abstract

We propose an unbiased estimator for $$P\left( X>Y\right) $$PX>Y and obtain an exact expression for its variance, based on judgement post stratification (JPS) sampling scheme. We then prove that the introduced estimator is consistent and establish its asymptotic normality. We show that the proposed estimator is at least as efficient asymptotically as its counterpart in simple random sampling (SRS), regardless of the quality of the rankings. For finite sample sizes, a Monte Carlo simulation study and a real data set are employed to show the preference of the JPS estimator to its SRS competitor in a wide range of settings.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:stpapr:v:61:y:2020:i:2:d:10.1007_s00362-017-0962-0
    DOI: 10.1007/s00362-017-0962-0
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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.
    9. 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.
    10. Eloísa Díaz-Francés & José Montoya, 2013. "The simplicity of likelihood based inferences for P(X > Y) and for the ratio of means in the exponential model," Statistical Papers, Springer, vol. 54(2), pages 499-522, May.
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