Large dimensional Spearman's rank correlation matrices: The central limit theorem and its applications
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915032541954048 |
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| author | Chen, Hantao Wang, Cheng |
| author_facet | Chen, Hantao Wang, Cheng |
| contents | This paper is concerned with Spearman's correlation matrices under large dimensional regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear spectral statistics of Spearman's correlation matrices, which extends the results of [\emph{Ann. Statist.} 43(2015) 2588--2623]. We also study the improved Spearman's correlation matrices [\emph{Ann. Math. Statist} 19(1948) 293--325] which is a standard U-statistic of order 3. As applications, we propose three new test statistics for large dimensional independent test and numerical studies demonstrate the applicability of our proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large dimensional Spearman's rank correlation matrices: The central limit theorem and its applications Chen, Hantao Wang, Cheng Statistics Theory 62H15, 62H20, 62G30, 62G35 This paper is concerned with Spearman's correlation matrices under large dimensional regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear spectral statistics of Spearman's correlation matrices, which extends the results of [\emph{Ann. Statist.} 43(2015) 2588--2623]. We also study the improved Spearman's correlation matrices [\emph{Ann. Math. Statist} 19(1948) 293--325] which is a standard U-statistic of order 3. As applications, we propose three new test statistics for large dimensional independent test and numerical studies demonstrate the applicability of our proposed methods. |
| title | Large dimensional Spearman's rank correlation matrices: The central limit theorem and its applications |
| topic | Statistics Theory 62H15, 62H20, 62G30, 62G35 |
| url | https://arxiv.org/abs/2411.15861 |