On the failure of the bootstrap for Chatterjee’s rank correlation
本文证明了在额外独立性假设下，标准自助法无法用于Chatterjee秩相关的不确定性估计，并提供了模拟证据，指出有效的推断方法是原检验或Lin & Han的渐近方差估计。
Abstract While researchers commonly use the bootstrap to quantify the uncertainty of an estimator, it has been noticed 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 the analytic asymptotic variance estimator of Lin & Han (2022) for more general purposes. [Received on 5 April 2023. Editorial decision on 10 January 2024]