# Limit theorems of Chatterjee's rank correlation

arXiv: https://arxiv.org/abs/2204.08031 · HTML: https://mlsanity.com/paper/2204.08031/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 17 Apr 2022.

## Builds on (most cited first, 5 of 5)

- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Efficient multivariate entropy estimation via k-nearest neighbour distances](https://mlsanity.com/paper/1606.00304/) (2016)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [On boosting the power of Chatterjee's rank correlation](https://mlsanity.com/paper/2108.06828/) (2021)
- [Exact Detection Thresholds and Minimax Optimality of Chatterjee's Correlation Coefficient](https://mlsanity.com/paper/2104.15140/) (2021)

## Built on by (most cited first, 3 of 3)

- [A survey of some recent developments in measures of association](https://mlsanity.com/paper/2211.04702/) (2022)
- [Variance reduction combining pre-experiment and in-experiment data](https://mlsanity.com/paper/2410.09027/) (2024)
- [Nearest-Neighbor Radii under Dependent Sampling](https://mlsanity.com/paper/2605.14343/) (2026)

## Abstract (arXiv)

Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is asymptotically normal as long as one variable is not a measurable function of the other, (b) the corresponding asymptotic variance is uniformly bounded by 36, and (c) a consistent variance estimator exists. Similar results also hold for Azadkia-Chatterjee's graph-based correlation coefficient, a multivariate analogue of Chatterjee's original proposal. The proof is given by appealing to H'ajek representation and Chatterjee's nearest-neighbor CLT.