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

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  • Shin-ichi Tsukada

    (Meisei University)

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.

Suggested Citation

  • Shin-ichi Tsukada, 2019. "High dimensional two-sample test based on the inter-point distance," Computational Statistics, Springer, vol. 34(2), pages 599-615, June.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-017-0777-4
    DOI: 10.1007/s00180-017-0777-4
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    References listed on IDEAS

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    10. Anil K. Ghosh & Munmun Biswas, 2016. "Distribution-free high-dimensional two-sample tests based on discriminating hyperplanes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 525-547, September.
    11. Munmun Biswas & Minerva Mukhopadhyay & Anil K. Ghosh, 2014. "A distribution-free two-sample run test applicable to high-dimensional data," Biometrika, Biometrika Trust, vol. 101(4), pages 913-926.
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    Cited by:

    1. Luai Al-Labadi & Forough Fazeli Asl & Zahra Saberi, 2022. "A Bayesian nonparametric multi-sample test in any dimension," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 217-242, June.
    2. Huang, Yuan & Li, Changcheng & Li, Runze & Yang, Songshan, 2022. "An overview of tests on high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Paul, Biplab & De, Shyamal K. & Ghosh, Anil K., 2022. "Some clustering-based exact distribution-free k-sample tests applicable to high dimension, low sample size data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Germán Aneiros & Ricardo Cao & Philippe Vieu, 2019. "Editorial on the special issue on Functional Data Analysis and Related Topics," Computational Statistics, Springer, vol. 34(2), pages 447-450, June.

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