On the failure of the bootstrap for Chatterjee's rank correlation

• 成果类型: Article
• 署名作者: Lin, Zhexiao; Han, Fang
• 署名单位: University of California System; University of California Berkeley; University of Washington; University of Washington Seattle
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asae004
• 发表日期: 2024
• 页码: 10631070
• 关键词: inconsistency; association; EFFICIENCY

摘要

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 for more general purposes.[Received on 5 April 2023. Editorial decision on 10 January 2024]