讲座题目：Central Limit Theorem for Linear Spectral Statistics of Large Dimensional Kendall’s Rank Correlation Matrices and Its Applications

讲座时间：2021/03/31 10:00-12:00

讲座人：李曾 副教授，南方科技大学统计与数据科学系

讲座简介：

In this talk we will talk about the limiting spectral behaviors of large dimensional Kendall’s rank correlation matrices generated by samples with independent and continuous components. The statistical setting 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 Marcenko-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.

讲座人简介：

李曾，南方科技大学统计与数据科学系副教授。2017年获得香港大学统计与精算学系博士学位，2017-2019年先后在美国华盛顿大学、宾夕法尼亚州立大学从事博士后研究工作，并于2019年入职南方科技大学。主要研究领域为随机矩阵理论、高维统计分析等，研究成果发表于The Annals of Statistics, Scandinavian Journal of Statistics 等国际统计学期刊。

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