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Multinomial interpoint distances

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  • Reza Modarres

    (The George Washington University)

Abstract

We explore the properties of the squared Euclidean interpoint distances (IDs) drawn from multinomial distributions. We consider the distances within one sample and across two samples and obtain their means, variances, covariances and distributions. We discuss applications of IDs for testing goodness of fit, the equality of high dimensional multinomial distributions, classification, and outliers detection. A simulation study compares the performance of the $$\chi ^2$$ χ 2 and the likelihood ratio statistics for testing equality of distributions, with methods based on the IDs.

Suggested Citation

  • Reza Modarres, 2018. "Multinomial interpoint distances," Statistical Papers, Springer, vol. 59(1), pages 341-360, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0766-7
    DOI: 10.1007/s00362-016-0766-7
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    References listed on IDEAS

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    1. Selvin, S. & Schulman, J. & Merrill, D.W., 1993. "Interpoint squared distance as a measure of spatial clustering," Social Science & Medicine, Elsevier, vol. 36(8), pages 1011-1016, April.
    2. Pietro Tebaldi & Marco Bonetti & Marcello Pagano, 2011. "M statistic commands: Interpoint distance distribution analysis," Stata Journal, StataCorp LP, vol. 11(2), pages 271-289, June.
    3. Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.
    4. Ye Dong & Stephen Lee, 2014. "Depth functions as measures of representativeness," Statistical Papers, Springer, vol. 55(4), pages 1079-1105, November.
    5. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    6. Liao, Shu-Min & Akritas, Michael, 2007. "Test-based classification: A linkage between classification and statistical testing," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1269-1281, July.
    7. Munmun Biswas & Minerva Mukhopadhyay & Anil K. Ghosh, 2014. "A distribution-free two-sample run test applicable to high-dimensional data," Biometrika, Biometrika Trust, vol. 101(4), pages 913-926.
    8. Zhenyu Liu & Reza Modarres, 2011. "Lens data depth and median," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1063-1074.
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