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Testing the equality of high dimensional distributions

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  • Modarres, Reza

Abstract

The Euclidean distance is not a suitable distance for high dimensional settings due to the distance concentration phenomenon. A novel statistic that is inspired by the interpoint distances, but avoids their computation, is proposed for comparing and visualizing high dimensional datasets. The new statistic is based on a high dimensional dissimilarity index that takes advantage of the concentration phenomenon. A simultaneous display of observations means and standard deviations that aids visualization, detection of suspect outliers, and enhances separability among the competing classes in the transformed space is discussed. The finite sample convergence of the dissimilarity indices is studied, nine statistics are compared under several distributions, and three applications are presented.

Suggested Citation

  • Modarres, Reza, 2025. "Testing the equality of high dimensional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:csdana:v:212:y:2025:i:c:s0167947325001215
    DOI: 10.1016/j.csda.2025.108245
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