{"ID":2883331,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.09040","arxiv_id":"2508.09040","title":"Bias correction for Chatterjee's graph-based correlation coefficient","abstract":"Azadkia and Chatterjee (2021) recently introduced a simple nearest neighbor (NN) graph-based correlation coefficient that consistently detects both independence and functional dependence. Specifically, it approximates a measure of dependence that equals 0 if and only if the variables are independent, and 1 if and only if they are functionally dependent. However, this NN estimator includes a bias term that may vanish at a rate slower than root-$n$, preventing root-$n$ consistency in general. In this article, we (i) analyze this bias term closely and show that it could become asymptotically negligible when the dimension is smaller than four; and (ii) propose a bias-correction procedure for more general settings. In both regimes, we obtain estimators (either the original or the bias-corrected version) that are root-$n$ consistent and asymptotically normal.","short_abstract":"Azadkia and Chatterjee (2021) recently introduced a simple nearest neighbor (NN) graph-based correlation coefficient that consistently detects both independence and functional dependence. Specifically, it approximates a measure of dependence that equals 0 if and only if the variables are independent, and 1 if and only...","url_abs":"https://arxiv.org/abs/2508.09040","url_pdf":"https://arxiv.org/pdf/2508.09040v2","authors":"[\"Mona Azadkia\",\"Leihao Chen\",\"Fang Han\"]","published":"2025-08-12T16:01:44Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"econ.EM\",\"math.ST\"]","methods":"[]","has_code":false}