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On a new multivariate two-sample test

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  • Baringhaus, L.
  • Franz, C.

Abstract

In this paper we propose a new test for the multivariate two-sample problem. The test statistic is the difference of the sum of all the Euclidean interpoint distances between the random variables from the two different samples and one-half of the two corresponding sums of distances of the variables within the same sample. The asymptotic null distribution of the test statistic is derived using the projection method and shown to be the limit of the bootstrap distribution. A simulation study includes the comparison of univariate and multivariate normal distributions for location and dispersion alternatives. For normal location alternatives the new test is shown to have power similar to that of the t- and T2-Test.

Suggested Citation

  • Baringhaus, L. & Franz, C., 2004. "On a new multivariate two-sample test," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 190-206, January.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:190-206
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    Citations

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    Cited by:

    1. Alba Fernández, V. & Jiménez Gamero, M.D. & Muñoz Garcia, J., 2008. "A test for the two-sample problem based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3730-3748, March.
    2. Van der Meulen, Sofie & Gaeremynck, Ann & Willekens, Marleen, 2007. "Attribute differences between U.S. GAAP and IFRS earnings: An exploratory study," The International Journal of Accounting, Elsevier, vol. 42(2), pages 123-142.
    3. Feng, Xingdong & Liu, Qiaochu & Wang, Caixing, 2023. "A lack-of-fit test for quantile regression process models," Statistics & Probability Letters, Elsevier, vol. 192(C).
    4. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian density forecasting of intraday electricity prices using multivariate skew t distributions," International Journal of Forecasting, Elsevier, vol. 24(4), pages 710-727.
    5. 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.
    6. Liu, Jicai & Si, Yuefeng & Niu, Yong & Zhang, Riquan, 2022. "Projection quantile correlation and its use in high-dimensional grouped variable screening," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    7. Petrie, Adam, 2016. "Graph-theoretic multisample tests of equality in distribution for high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 145-158.
    8. Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.
    9. Sexton, Joseph & Blomhoff, Rune & Karlsen, Anette & Laake, Petter, 2012. "Adaptive combination of dependent tests," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1935-1943.
    10. 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.
    11. V. Alba Fernández & D. Barrera Rosillo & M. Ibáñez Pérez & M. Jiménez Gamero, 2009. "A homogeneity test for bivariate random variables," Computational Statistics, Springer, vol. 24(3), pages 513-531, August.
    12. Sunil Mathur, 2009. "A new nonparametric bivariate test for two sample location problem," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(3), pages 375-388, August.
    13. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(2), pages 153-177, June.
    14. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    15. Qiu, Tao & Zhang, Qintong & Fang, Yuanyuan & Xu, Wangli, 2024. "Testing homogeneity in high dimensional data through random projections," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    16. 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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