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Universally consistent K-sample tests via dependence measures

Author

Listed:
  • Panda, Sambit
  • Shen, Cencheng
  • Perry, Ronan
  • Zorn, Jelle
  • Lutz, Antoine
  • Priebe, Carey E.
  • Vogelstein, Joshua T.

Abstract

The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent methods to test distributional differences. In this paper, we demonstrate the existence of a transformation that allows K-sample testing to be carried out using any dependence measure. Consequently, universally consistent K-sample testing can be achieved using a universally consistent dependence measure, such as distance correlation and the Hilbert–Schmidt independence criterion. This enables a wide range of dependence measures to be easily applied to K-sample testing.

Suggested Citation

  • Panda, Sambit & Shen, Cencheng & Perry, Ronan & Zorn, Jelle & Lutz, Antoine & Priebe, Carey E. & Vogelstein, Joshua T., 2025. "Universally consistent K-sample tests via dependence measures," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002475
    DOI: 10.1016/j.spl.2024.110278
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    References listed on IDEAS

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    1. Cencheng Shen & Carey E. Priebe & Joshua T. Vogelstein, 2020. "From Distance Correlation to Multiscale Graph Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 280-291, January.
    2. Zhou Zhou, 2012. "Measuring nonlinear dependence in time‐series, a distance correlation approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 438-457, May.
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    4. Székely, Gábor J. & Rizzo, Maria L., 2013. "The distance correlation t-test of independence in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 193-213.
    5. Xueqin Wang & Wenliang Pan & Wenhao Hu & Yuan Tian & Heping Zhang, 2015. "Conditional Distance Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1726-1734, December.
    6. Wenliang Pan & Xueqin Wang & Heping Zhang & Hongtu Zhu & Jin Zhu, 2020. "Ball Covariance: A Generic Measure of Dependence in Banach Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 307-317, January.
    7. Youjin Lee & Cencheng Shen & Carey E Priebe & Joshua T Vogelstein, 2019. "Network dependence testing via diffusion maps and distance-based correlations," Biometrika, Biometrika Trust, vol. 106(4), pages 857-873.
    8. Cencheng Shen & Joshua T. Vogelstein, 2021. "The exact equivalence of distance and kernel methods in hypothesis testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 385-403, September.
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