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Analysis of distance matrices

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  • Modarres, Reza

Abstract

The relationships between eigenvalues of the distance matrices and outliers are largely unexplored. We show a discrepancy in the sizes of eigenvalues of the distance matrix that is contaminated with outliers. We present test statistics to determine when a distance matrix has a constant structure. We relate the eigenvalues of the two-sample distance matrix to the tests of equality of distributions, study dissimilarity matrices and their eigenvalues in high dimensional and low sample size setting.

Suggested Citation

  • Modarres, Reza, 2023. "Analysis of distance matrices," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002334
    DOI: 10.1016/j.spl.2022.109720
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    References listed on IDEAS

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    1. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    2. 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.
    3. Lingzhe Guo & Reza Modarres, 2019. "Interpoint Distance Classification of High Dimensional Discrete Observations," International Statistical Review, International Statistical Institute, vol. 87(2), pages 191-206, August.
    4. Reza Modarres, 2020. "Graphical Comparison of High‐Dimensional Distributions," International Statistical Review, International Statistical Institute, vol. 88(3), pages 698-714, December.
    5. Reza Modarres, 2022. "Nonparametric tests for detection of high dimensional outliers," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 34(1), pages 206-227, January.
    6. Marco Marozzi & Amitava Mukherjee & Jan Kalina, 2020. "Interpoint distance tests for high-dimensional comparison studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(4), pages 653-665, March.
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