Limit theorems of Chatterjee's rank correlation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908391881834496 |
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| author | Lin, Zhexiao Han, Fang |
| author_facet | Lin, Zhexiao Han, Fang |
| contents | Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is asymptotically normal as long as one variable is not a measurable function of the other, (b) the corresponding asymptotic variance is uniformly bounded by 36, and (c) a consistent variance estimator exists. Similar results also hold for Azadkia-Chatterjee's graph-based correlation coefficient, a multivariate analogue of Chatterjee's original proposal. The proof is given by appealing to Hájek representation and Chatterjee's nearest-neighbor CLT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_08031 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Limit theorems of Chatterjee's rank correlation Lin, Zhexiao Han, Fang Statistics Theory Machine Learning Probability Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is asymptotically normal as long as one variable is not a measurable function of the other, (b) the corresponding asymptotic variance is uniformly bounded by 36, and (c) a consistent variance estimator exists. Similar results also hold for Azadkia-Chatterjee's graph-based correlation coefficient, a multivariate analogue of Chatterjee's original proposal. The proof is given by appealing to Hájek representation and Chatterjee's nearest-neighbor CLT. |
| title | Limit theorems of Chatterjee's rank correlation |
| topic | Statistics Theory Machine Learning Probability |
| url | https://arxiv.org/abs/2204.08031 |