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Limit theorems of Chatterjee's rank correlation

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arxiv 2204.08031 v4 pith:NO43MHOO submitted 2022-04-17 math.ST cs.LGmath.PRstat.TH

Zhexiao Lin , Fang Han This is my paper · ORCID
classification math.STcs.LGmath.PRstat.TH
keywords chatterjeecorrelationrankvarianceajekanalogueappealingasymptotic
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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.

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Cited by 2 Pith papers

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