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Asymptotic normality of interpoint distances for high-dimensional data with applications to the two-sample problem

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  • Jun Li

Abstract

SummaryInterpoint distances have applications in many areas of probability and statistics. Thanks to their simplicity of computation, interpoint distance-based procedures are particularly appealing for analysing small samples of high-dimensional data. In this paper, we first study the asymptotic distribution of interpoint distances in the high-dimension, low-sample-size setting and show that it is normal under regularity conditions. We then construct a powerful test for the two-sample problem, which is consistent for detecting location and scale differences. Simulations show that the test compares favourably with existing distance-based tests.

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  • 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.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:529-546.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy020
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    References listed on IDEAS

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    Cited by:

    1. Modarres, Reza, 2023. "Analysis of distance matrices," Statistics & Probability Letters, Elsevier, vol. 193(C).

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