TRACY-WIDOM LIMIT FOR KENDALL'S TAU

• 成果类型: Article
• 署名作者: Bao, Zhigang
• 署名单位: Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1786
• 发表日期: 2019
• 页码: 3504-3532
• 关键词: sample covariance matrices; LARGEST EIGENVALUE; principal components; edge universality; fluctuations

摘要

In this paper, we study a high-dimensional random matrix model from nonparametric statistics called the Kendall rank correlation matrix, which is a natural multivariate extension of the Kendall rank correlation coefficient. We establish the Tracy-Widom law for its largest eigenvalue. It is the first Tracy-Widom law for a nonparametric random matrix model, and also the first Tracy-Widom law for a high-dimensional U-statistic.