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On the interpoint distances of Bernoulli vectors

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  • Modarres, Reza

Abstract

We consider the squared Euclidean interpoint distances (IDs) among multivariate Bernoulli observations and determine the mean, covariance and the distribution of the IDs within a single group or across two groups. We discuss testing the equality of two distribution functions when the number of variables is large and exceeds the number of observations.

Suggested Citation

  • Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:215-222
    DOI: 10.1016/j.spl.2013.10.012
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    References listed on IDEAS

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    1. Baringhaus, L. & Franz, C., 2004. "On a new multivariate two-sample test," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 190-206, January.
    2. Paul R. Rosenbaum, 2005. "An exact distribution‐free test comparing two multivariate distributions based on adjacency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 515-530, September.
    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. J. C. Gower & G. J. S. Ross, 1969. "Minimum Spanning Trees and Single Linkage Cluster Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 18(1), pages 54-64, March.
    5. Modarres, Reza, 2011. "High-dimensional generation of Bernoulli random vectors," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1136-1142, August.
    6. Liu, Zhenyu & Modarres, Reza & Yang, Mengta, 2013. "A multivariate control quantile test using data depth," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 262-270.
    7. Caroni, C. & Prescott, P., 1995. "On Rohlf's Method for the Detection of Outliers in Multivariate Data," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 295-307, February.
    8. J. D. Wilbur & J. K. Ghosh & C. H. Nakatsu & S. M. Brouder & R. W. Doerge, 2002. "Variable Selection in High-Dimensional Multivariate Binary Data with Application to the Analysis of Microbial Community DNA Fingerprints," Biometrics, The International Biometric Society, vol. 58(2), pages 378-386, June.
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    Cited by:

    1. Modarres, Reza, 2016. "Multivariate Poisson interpoint distances," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 113-123.
    2. Mengta Yang & Reza Modarres, 2017. "Multivariate tests of uniformity," Statistical Papers, Springer, vol. 58(3), pages 627-639, September.
    3. Reza Modarres, 2018. "Multinomial interpoint distances," Statistical Papers, Springer, vol. 59(1), pages 341-360, March.

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