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Mallows’ models for imperfect ranking in ranked set sampling

Author

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  • Nikolay I. Nikolov

    (Bulgarian Academy of Sciences)

  • Eugenia Stoimenova

    (Bulgarian Academy of Sciences)

Abstract

In this paper, we consider some statistical measures of deviation from the perfect ranking in the framework of ranked set sampling. We use nonparametric approach for testing the null hypothesis for perfect ranking. The distance-based Mallows’ models with appropriate distance on permutations are suggested in the case of imperfect ranking. Some asymptotic results for the corresponding error probability matrix are derived for the models based on Spearman’s footrule and Spearman’s rho. We propose an EM algorithm for estimating the unknown parameter in the Mallows’ models in order to compare the power of the presented test statistics.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:3:d:10.1007_s10182-019-00354-4
    DOI: 10.1007/s10182-019-00354-4
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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. Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    3. Zamanzade, Ehsan & Arghami, Nasser Reza & Vock, Michael, 2012. "Permutation-based tests of perfect ranking," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2213-2220.
    4. Nikolay I. Nikolov & Eugenia Stoimenova, 2019. "Asymptotic properties of Lee distance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(3), pages 385-408, April.
    5. Omer Ozturk, 2010. "Nonparametric maximum-likelihood estimation of within-set ranking errors in ranked set sampling," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 823-840.
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