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Multivariate power series interpoint distances

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  • Reza Modarres

    (George Washington University)

  • Yu Song

    (George Washington University)

Abstract

We establish (a) the probability mass function of the interpoint distance (IPD) between random vectors that are drawn from the multivariate power series family of distributions (MPSD); (b) obtain the distribution of the IPD within one sample and across two samples from this family; (c) determine the distribution of the MPSD Euclidean norm and distance from fixed points in $${\mathbb {Z}}^d$$ Z d ; and (d) provide the distribution of the IPDs of vectors drawn from a mixture of the MPSD distributions. We present a method for testing the homogeneity of MPSD mixtures using the sample IPDs.

Suggested Citation

  • Reza Modarres & Yu Song, 2020. "Multivariate power series interpoint distances," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 955-982, December.
    • Handle: RePEc:spr:stmapp:v:29:y:2020:i:4:d:10.1007_s10260-020-00508-8
    DOI: 10.1007/s10260-020-00508-8
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    References listed on IDEAS

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    1. 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.
    2. Berrendero, José R. & Cuevas, Antonio & Pateiro-López, Beatriz, 2016. "Shape classification based on interpoint distance distributions," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 237-247.
    3. Zhenyu Liu & Reza Modarres, 2011. "A triangle test for equality of distribution functions in high dimensions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 605-615.
    4. W. Lok & Stephen Lee, 2011. "A new statistical depth function with applications to multimodal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 617-631.
    5. Hall, Peter & Titterington, D. M. & Xue, Jing-Hao, 2009. "Median-Based Classifiers for High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1597-1608.
    6. Zhang, Peng & Wang, Xiaogang & Song, Peter X.K., 2006. "Clustering Categorical Data Based on Distance Vectors," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 355-367, March.
    7. Peter Hall, 2002. "Permutation tests for equality of distributions in high-dimensional settings," Biometrika, Biometrika Trust, vol. 89(2), pages 359-374, June.
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