IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i1d10.1007_s00362-016-0766-7.html
   My bibliography  Save this article

Multinomial interpoint distances

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0766-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0766-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Zhenyu Liu & Reza Modarres, 2011. "Lens data depth and median," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1063-1074.
    7. Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.
    8. Ye Dong & Stephen Lee, 2014. "Depth functions as measures of representativeness," Statistical Papers, Springer, vol. 55(4), pages 1079-1105, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Modarres, Reza, 2016. "Multivariate Poisson interpoint distances," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 113-123.
    2. Saha, Enakshi & Sarkar, Soham & Ghosh, Anil K., 2017. "Some high-dimensional one-sample tests based on functions of interpoint distances," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 83-95.
    3. Nicolas Städler & Sach Mukherjee, 2017. "Two-sample testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 225-246, January.
    4. Banerjee, Bilol, 2024. "Testing distributional equality for functional random variables," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    5. Shin-ichi Tsukada, 2019. "High dimensional two-sample test based on the inter-point distance," Computational Statistics, Springer, vol. 34(2), pages 599-615, June.
    6. Ludwig Baringhaus & Norbert Henze, 2016. "Revisiting the two-sample runs test," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 432-448, September.
    7. Mondal, Pronoy K. & Biswas, Munmun & Ghosh, Anil K., 2015. "On high dimensional two-sample tests based on nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 168-178.
    8. Jun Li, 2018. "Asymptotic normality of interpoint distances for high-dimensional data with applications to the two-sample problem," Biometrika, Biometrika Trust, vol. 105(3), pages 529-546.
    9. Cousido-Rocha, Marta & de Uña-Álvarez, Jacobo & Hart, Jeffrey D., 2019. "A two-sample test for the equality of univariate marginal distributions for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    10. Mengta Yang & Reza Modarres, 2017. "Multivariate tests of uniformity," Statistical Papers, Springer, vol. 58(3), pages 627-639, September.
    11. Paul, Biplab & De, Shyamal K. & Ghosh, Anil K., 2022. "Some clustering-based exact distribution-free k-sample tests applicable to high dimension, low sample size data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    12. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2024. "Testing equality of several distributions in separable metric spaces: A maximum mean discrepancy based approach," Journal of Econometrics, Elsevier, vol. 239(2).
    13. Reza Modarres, 2024. "Hotelling $$T^2$$ T 2 test in high dimensions with application to Wilks outlier method," Statistical Papers, Springer, vol. 65(8), pages 5203-5218, October.
    14. Fraiman, Ricardo & Gamboa, Fabrice & Moreno, Leonardo, 2019. "Connecting pairwise geodesic spheres by depth: DCOPS," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 81-94.
    15. Qiu, Tao & Zhang, Qintong & Fang, Yuanyuan & Xu, Wangli, 2024. "Testing homogeneity in high dimensional data through random projections," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    16. Stefano Bonnini & Getnet Melak Assegie & Kamila Trzcinska, 2024. "Review about the Permutation Approach in Hypothesis Testing," Mathematics, MDPI, vol. 12(17), pages 1-29, August.
    17. Lingzhe Guo & Reza Modarres, 2020. "Testing the equality of matrix distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 289-307, June.
    18. Kevin Leckey & Dennis Malcherczyk & Melanie Horn & Christine H. Müller, 2023. "Simple powerful robust tests based on sign depth," Statistical Papers, Springer, vol. 64(3), pages 857-882, June.
    19. 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.
    20. Xu Li & Wenjuan Hu & Baoxue Zhang, 2023. "Measuring and testing homogeneity of distributions by characteristic distance," Statistical Papers, Springer, vol. 64(2), pages 529-556, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0766-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.