Universally consistent K-sample tests via dependence measures

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

Statistics & Probability Letters, 2025, vol. 216, issue C

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.

Keywords: K-sample testing; Testing independence; Dependence measure (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110278

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