While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation. In this paper, we provide proof of this issue under an additional independence assumption, and complement our theory with simulation evidence for general settings. Chatterjee's rank correlation thus falls into a category of statistics that are asymptotically normal but bootstrap inconsistent. Valid inferential methods in this case are Chatterjee's original proposal (for testing independence) and Lin and Han (2022)'s analytic asymptotic variance estimator (for more general purposes).

翻译：Translated abstract: 尽管研究人员通常使用自助法进行统计推断，但我们许多人已经意识到，一般来说，标准自助法不能很好地处理Chatterjee的排名相关性。在本文中，我们在附加独立性假设下提供了这个问题的证明，并结合一般情况下的模拟证据来补充我们的理论。因此，Chatterjee的排名相关性属于渐近正态但不具备自助法一致性的统计学类别。在这种情况下，合法的推断方法包括Chatterjee的原始提议（用于测试独立性）和Lin和Han（2022）的解析渐近方差估计器（用于更一般的目的）。