2025/08/12 by Mona Azadkia, Azadkia, Mona, Fang Han +2
Mathematics · Computer Science · #Statistical Methods and Inference #Data Analysis with R #Advanced Statistical Modeling Techniques
paper · pdf · doi:10.48550/arxiv.2508.09040
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.