Limit theorems of Chatterjee's rank correlation

2022/04/17 by Lin, Zhexiao, Han, Fang · 3 citations
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2204.08031

Abstract

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 Hájek representation and Chatterjee's nearest-neighbor CLT.

Cited by

• An ordering for the strength of functional dependence
• Bias correction for Chatterjee's graph-based correlation coefficient
• The exact region and an inequality between Chatterjee's and Spearman's rank correlations

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