Bias correction for Chatterjee's graph-based correlation coefficient

Mona Azadkia, Leihao Chen and Fang Han

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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 propose a bias correction approach that overcomes this limitation, yielding an NN-based estimator that is both root-$n$ consistent and asymptotically normal.

Date: 2025-08
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