Spectral analysis of large dimensional Chatterjee's rank correlation matrix
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909831566196736 |
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| author | Dong, Zhaorui Han, Fang Yao, Jianfeng |
| author_facet | Dong, Zhaorui Han, Fang Yao, Jianfeng |
| contents | This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the empirical spectral distribution of its symmetrized version converges to the semicircle law, and thus providing the first example of a large correlation matrix deviating from the Marchenko-Pastur law that governs those of Pearson, Kendall, and Spearman. We further establish central limit theorems for linear spectral statistics, which in turn enable the development of Chatterjee's rank correlation-based tests of complete independence among the components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral analysis of large dimensional Chatterjee's rank correlation matrix Dong, Zhaorui Han, Fang Yao, Jianfeng Statistics Theory Probability This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the empirical spectral distribution of its symmetrized version converges to the semicircle law, and thus providing the first example of a large correlation matrix deviating from the Marchenko-Pastur law that governs those of Pearson, Kendall, and Spearman. We further establish central limit theorems for linear spectral statistics, which in turn enable the development of Chatterjee's rank correlation-based tests of complete independence among the components. |
| title | Spectral analysis of large dimensional Chatterjee's rank correlation matrix |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2510.07262 |