AZADKIA-CHATTERJEE'S CORRELATION COEFFICIENT ADAPTS TO MANIFOLD DATA

• 成果类型: Article
• 署名作者: Han, Fang; Huang, Zhihan
• 署名单位: University of Washington; University of Washington Seattle; University of Pennsylvania
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2088
• 发表日期: 2024
• 页码: 5172-5210
• 关键词: dependence

摘要

In their seminal work, Azadkia and Chatterjee ( Ann. Statist. 49 (2021) 3070-3102) initiated graph-based methods for measuring variable dependence strength. By appealing to nearest neighbor graphs based on the Euclidean metric, they gave an elegant solution to a problem of R & eacute;nyi ( Acta Math. Acad. Sci. Hung. 10 (1959) 441-451). This idea was later developed in Deb, Ghosal and Sen (2020) (https://arxiv.org/abs/2010.01768) and the authors there proved that, quite interestingly, Azadkia and Chatterjee's correlation coefficient can automatically adapt to the manifold structure of the data. This paper furthers their study in terms of calculating the statistic's limiting variance under independence-showing that it only depends on the manifold dimension-and extending this distribution-free property to a class of metrics beyond the Euclidean.