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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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    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. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    3. Paul R. Rosenbaum, 2005. "An exact distribution‐free test comparing two multivariate distributions based on adjacency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 515-530, September.
    4. Zhenyu Liu & Reza Modarres, 2011. "A triangle test for equality of distribution functions in high dimensions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 605-615.
    5. Mondal, Pronoy K. & Biswas, Munmun & Ghosh, Anil K., 2015. "On high dimensional two-sample tests based on nearest neighbors," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 168-178.
    6. 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.
    7. Rousson, Valentin, 2002. "On Distribution-Free Tests for the Multivariate Two-Sample Location-Scale Model," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 43-57, January.
    8. Lan Wang & Bo Peng & Runze Li, 2015. "A High-Dimensional Nonparametric Multivariate Test for Mean Vector," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1658-1669, December.
    9. Srivastava, Muni S., 2009. "A test for the mean vector with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 518-532, March.
    10. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    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.
    12. Peter Hall, 2002. "Permutation tests for equality of distributions in high-dimensional settings," Biometrika, Biometrika Trust, vol. 89(2), pages 359-374, June.
    13. Srivastava, Muni S. & Katayama, Shota & Kano, Yutaka, 2013. "A two sample test in high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 349-358.
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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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).

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