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 and independent data; furthermore, simulations indicate that it also performs well for discrete and dependent data, and that it outperforms alternative estimation methods.

翻译：我们证明，只要Chatterjee秩相关系数的渐近正态性成立，则针对该系数的$m$ out of $n$自助法是一致的。特别地，我们证明$m$ out of $n$自助法既适用于连续数据，也适用于离散独立数据；此外，模拟表明该方法在离散相依数据上同样表现良好，且优于其他估计方法。