Azadkia and Chatterjee (Azadkia and Chatterjee, 2021) recently introduced a graph-based correlation coefficient that has garnered significant attention. The method relies on a nearest neighbor graph (NNG) constructed from the data. While appealing in many respects, NNGs typically lack the desirable property of scale invariance; that is, changing the scales of certain covariates can alter the structure of the graph. This paper addresses this limitation by employing a rank-based NNG proposed by Rosenbaum (2005) and gives necessary theoretical guarantees for the corresponding rank-based Azadkia-Chatterjee correlation coefficient.

翻译：Azadkia与Chatterjee（Azadkia and Chatterjee, 2021）近期提出了一种基于图的相关系数，引起了广泛关注。该方法依赖于从数据构建的最近邻图（NNG）。尽管在许多方面具有吸引力，但NNG通常缺乏尺度不变性这一理想性质；即改变某些协变量的尺度可能会改变图的结构。本文通过采用Rosenbaum（2005）提出的基于秩的NNG来解决这一局限性，并为相应的基于秩的Azadkia-Chatterjee相关系数提供了必要的理论保证。