We prove that an $m$ out of $n$ bootstrap procedure for Chatterjee's rank correlation is consistent whenever asymptotic normality of Chatterjee's rank correlation can be established. In particular, we prove that $m$ out of $n$ bootstrap works for continuous as well as for discrete data with independent coordinates; furthermore, simulations indicate that it also performs well for discrete data with dependent coordinates, and that it outperforms alternative estimation methods. Consistency of the bootstrap is proved in the Kolmogorov as well as in the Wasserstein distance.

翻译：我们证明了当Chatterjee秩相关可建立渐近正态性时，针对该相关系数的$m$ out of $n$自助法具有一致性。具体地，我们证明了$m$ out of $n$自助法适用于连续数据以及坐标独立的高散数据；此外，模拟结果表明该方法在坐标相依的离散数据上同样表现良好，且优于其他估计方法。自助法的一致性在Kolmogorov距离与Wasserstein距离下均得到证明。