On a rank-based Azadkia-Chatterjee correlation coefficient
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910725832704000 |
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| author | Tran, Leon Han, Fang |
| author_facet | Tran, Leon Han, Fang |
| contents | Azadkia and Chatterjee (Azadkia and Chatterjee, 2021) recently introduced a graph-based correlation coefficient that has garnered significant attention. The method relies on a nearest neighbor graph (NNG) constructed from the data. While appealing in many respects, NNGs typically lack the desirable property of scale invariance; that is, changing the scales of certain covariates can alter the structure of the graph. This paper addresses this limitation by employing a rank-based NNG proposed by Rosenbaum (2005) and gives necessary theoretical guarantees for the corresponding rank-based Azadkia-Chatterjee correlation coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a rank-based Azadkia-Chatterjee correlation coefficient Tran, Leon Han, Fang Statistics Theory Azadkia and Chatterjee (Azadkia and Chatterjee, 2021) recently introduced a graph-based correlation coefficient that has garnered significant attention. The method relies on a nearest neighbor graph (NNG) constructed from the data. While appealing in many respects, NNGs typically lack the desirable property of scale invariance; that is, changing the scales of certain covariates can alter the structure of the graph. This paper addresses this limitation by employing a rank-based NNG proposed by Rosenbaum (2005) and gives necessary theoretical guarantees for the corresponding rank-based Azadkia-Chatterjee correlation coefficient. |
| title | On a rank-based Azadkia-Chatterjee correlation coefficient |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2412.02668 |