Bias correction for Chatterjee's graph-based correlation coefficient

Mona Azadkia, Leihao Chen and Fang Han

Papers from arXiv.org

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.

Date: 2025-08, Revised 2026-01
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2508.09040 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2508.09040

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().