IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v216y2025ics0167715224002475.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224002475
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2024.110278?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    3. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Dingke Tang & Dehan Kong & Wenliang Pan & Linbo Wang, 2023. "Ultra‐high dimensional variable selection for doubly robust causal inference," Biometrics, The International Biometric Society, vol. 79(2), pages 903-914, June.
    3. Xu, Kai & Cheng, Qing, 2024. "Test of conditional independence in factor models via Hilbert–Schmidt independence criterion," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    4. Lai, Tingyu & Zhang, Zhongzhan & Wang, Yafei & Kong, Linglong, 2021. "Testing independence of functional variables by angle covariance," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    5. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2017. "Distance correlation coefficients for Lancaster distributions," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 19-39.
    6. Mirosław Krzyśko & Łukasz Smaga, 2024. "Application of distance standard deviation in functional data analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 431-454, June.
    7. Chaudhuri, Arin & Hu, Wenhao, 2019. "A fast algorithm for computing distance correlation," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 15-24.
    8. Yuan, Qingcong & Chen, Xianyan & Ke, Chenlu & Yin, Xiangrong, 2022. "Independence index sufficient variable screening for categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    9. Xuewei Cheng & Gang Li & Hong Wang, 2024. "The concordance filter: an adaptive model-free feature screening procedure," Computational Statistics, Springer, vol. 39(5), pages 2413-2436, July.
    10. Ke, Chenlu & Yang, Wei & Yuan, Qingcong & Li, Lu, 2023. "Partial sufficient variable screening with categorical controls," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    11. Shang, Du & Shang, Pengjian, 2022. "The dependence measurements based on martingale difference correlation and distance correlation: Efficient tools to distinguish different complex systems," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    12. Matsui, Muneya & Mikosch, Thomas & Roozegar, Rasool & Tafakori, Laleh, 2022. "Distance covariance for random fields," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 280-322.
    13. Yi Liu & Qihua Wang, 2018. "Model-free feature screening for ultrahigh-dimensional data conditional on some variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 283-301, April.
    14. Zhou, Yeqing & Liu, Jingyuan & Zhu, Liping, 2020. "Test for conditional independence with application to conditional screening," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    15. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2015. "A generalization of an integral arising in the theory of distance correlation," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 116-119.
    16. Jun Lu & Lu Lin, 2020. "Model-free conditional screening via conditional distance correlation," Statistical Papers, Springer, vol. 61(1), pages 225-244, February.
    17. Guochang Wang & Wai Keung Li & Ke Zhu, 2018. "New HSIC-based tests for independence between two stationary multivariate time series," Papers 1804.09866, arXiv.org.
    18. Wan, Phyllis & Davis, Richard A., 2022. "Goodness-of-fit testing for time series models via distance covariance," Journal of Econometrics, Elsevier, vol. 227(1), pages 4-24.
    19. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    20. Hung Hung & Su‐Yun Huang, 2019. "Sufficient dimension reduction via random‐partitions for the large‐p‐small‐n problem," Biometrics, The International Biometric Society, vol. 75(1), pages 245-255, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002475. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.