{"ID":2858917,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.07262","arxiv_id":"2510.07262","title":"Spectral analysis of large dimensional Chatterjee's rank correlation matrix","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.07262","url_pdf":"https://arxiv.org/pdf/2510.07262v1","authors":"[\"Zhaorui Dong\",\"Fang Han\",\"Jianfeng Yao\"]","published":"2025-10-08T17:23:55Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}