{"ID":2871812,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.10268","arxiv_id":"2509.10268","title":"Quantifying and testing dependence to categorical variables","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 $χ^2$-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.","short_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 $χ^2$-distribution i...","url_abs":"https://arxiv.org/abs/2509.10268","url_pdf":"https://arxiv.org/pdf/2509.10268v2","authors":"[\"Siegfried Hörmann\",\"Daniel Strenger-Galvis\"]","published":"2025-09-12T14:10:05Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}