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：尽管研究者常采用自助法进行统计推断，但许多人已意识到标准自助法通常不适用于Chatterjee秩相关。本文在额外独立性假设下证明了该问题，并通过仿真实验佐证了一般情形下的理论结论。由此，Chatterjee秩相关属于一类渐近正态但自助法不一致的统计量。对此类统计量有效的推断方法包括Chatterjee原始提议（用于独立性检验）及Lin与Han（2022）提出的解析渐近方差估计量（适用于更广泛场景）。