CENTRAL LIMIT THEOREM FOR LINEAR SPECTRAL STATISTICS OF LARGE DIMENSIONAL KENDALL'S RANK CORRELATION MATRICES AND ITS APPLICATIONS

• 成果类型: Article
• 署名作者: Li, Zeng; Wang, Qinwen; Li, Runze
• 署名单位: Southern University of Science & Technology; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2013
• 发表日期: 2021
• 页码: 1569-1593
• 关键词: INDEPENDENCE; tests; ratio; clt

摘要

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. The statistical setting in this paper covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of the Kendall's rank correlation matrices under the Marchenko-Pastur asymptotic regime, in which the dimension diverges to infinity proportionally with the sample size. We further propose three nonparametric procedures for high dimensional independent test and their limiting null distributions are derived by implementing this CLT. Our numerical comparisons demonstrate the robustness and superiority of our proposed test statistics under various mixed and heavy-tailed cases.