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Most powerful rank tests for perfect rankings

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  • Frey, Jesse
  • Wang, Le

Abstract

We consider the problem of testing for perfect rankings in ranked set sampling (RSS). By using a new algorithm for computing the probability that specified independent random variables have a particular ordering, we find most powerful rank tests of the null hypothesis of perfect rankings against fully specified alternatives. We compare the power of these most powerful rank tests to that of existing rank tests in the literature, and we find that the existing tests are surprisingly close to optimal over a wide range of alternatives to perfect rankings. This finding holds both for balanced RSS and for unbalanced RSS cases where the different ranks are not equally represented in the sample. We find that the best of the existing tests is the test that rejects when the null probability of the observed ranks is small, and we provide a new, more efficient R function for computing the test statistic.

Suggested Citation

  • Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    • Handle: RePEc:eee:csdana:v:60:y:2013:i:c:p:157-168
    DOI: 10.1016/j.csda.2012.11.012
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    References listed on IDEAS

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    1. Frey, Jesse & Ozturk, Omer & Deshpande, Jayant V., 2007. "Nonparametric Tests for Perfect Judgment Rankings," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 708-717, June.
    2. 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.
    3. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    4. 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.
    5. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, 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. 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.
    3. 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.
    4. Hamid Rahmani & Mostafa Razmkhah, 2017. "Perfect ranking test in moving extreme ranked set sampling," Statistical Papers, Springer, vol. 58(3), pages 855-875, September.
    5. Saeid Amiri & Reza Modarres & Silvelyn Zwanzig, 2017. "Tests of perfect judgment ranking using pseudo-samples," Computational Statistics, Springer, vol. 32(4), pages 1309-1322, December.
    6. Nikolay I. Nikolov & Eugenia Stoimenova, 2020. "Mallows’ models for imperfect ranking in ranked set sampling," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 459-484, September.

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