Quantifying and testing dependence to categorical variables
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911188425637888 |
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| author | Hörmann, Siegfried Strenger-Galvis, Daniel |
| author_facet | Hörmann, Siegfried Strenger-Galvis, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantifying and testing dependence to categorical variables Hörmann, Siegfried Strenger-Galvis, Daniel Statistics Theory 62H20 (Primary) 62G05, 62G10 (Secondary) 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. |
| title | Quantifying and testing dependence to categorical variables |
| topic | Statistics Theory 62H20 (Primary) 62G05, 62G10 (Secondary) |
| url | https://arxiv.org/abs/2509.10268 |