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arXiv · 2509.10268

Quantifying and testing dependence to categorical variables

Siegfried Hörmann·Daniel Strenger-Galvis
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Abstract

We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator. Moreover, we develop an independence test which has an asymptotic $\chi^2$-distribution if the variables are independent and prove that this test is consistent against any violation of independence. The test is also applicable to the classical~$K$-sample problem with possibly high- or infinite-dimensional distributions. We discuss some extensions, including a variant of the coefficient for measuring conditional dependence.

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Siegfried Hörmann, Daniel Strenger-Galvis. 2025-09-12. Quantifying and testing dependence to categorical variables. https://arxiv.org/abs/2509.10268

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