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High dimensional two-sample test based on the inter-point distance

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Abstract

The multivariate two-sample problem has been extensively investigated, and various methods have been proposed. However, most two-sample tests perform poorly when applied to high-dimensional data, and many of them are not applicable when the dimension of the data exceeds the sample size. We reconsider two previously reported tests (Baringhaus and Franz in Stat Sin 20:1333–1361, 2010; Biswas and Ghosh in J Multivar Anal 123:160–171, 2014), and propose two new criteria. Simulations demonstrate that the power of the proposed test is stable for high-dimensional data and large samples, and the power of our test is equivalent to that of the test by Biswas and Ghosh when the covariance matrices are different. We also investigate the theoretical properties of our test when the dimension tends to infinity and the sample size is fixed, and when the dimension is fixed and the sample size tends to infinity. In these cases, the proposed test is asymptotically distribution-free and consistent.

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Acknowledgements

The author would like to thank the referees sincerely for their careful reading and numerous valuable comments that helped to improve the original manuscript.

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Authors and Affiliations

  1. School of Education, Meisei University, 2-1-1 Hodokubo Hino, Tokyo, 191-8506, Japan

    Shin-ichi Tsukada

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  1. Shin-ichi Tsukada
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Correspondence to Shin-ichi Tsukada.

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Tsukada, Si. High dimensional two-sample test based on the inter-point distance. Comput Stat 34, 599–615 (2019). https://doi.org/10.1007/s00180-017-0777-4

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