论文标题
限制Chatterjee等级相关的定理
Limit theorems of Chatterjee's rank correlation
论文作者
论文摘要
许多许多人热切期待着一般（可能是非独立的随机变量），建立Chatterjee等级相关性的限制分布。本文表明，（a）Chatterjee的等级相关性是渐近正常的，只要一个变量不是另一个变量的函数，（b）相应的渐近方差在36中均匀地界定，并且（c）（c）一致的方差估计值存在。 Azadkia-Chatterjee的基于图的相关系数也具有类似的结果，这是Chatterjee原始建议的多元类似物。该证明是通过吸引Hájek代表和Chatterjee最近的邻居CLT给出的。
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.
