Abstract: Consider Schott's statistic （Schott, 2005) defined as the squared Frobenius norm of the sample correlation matrix for data from $\alpha$-regularly varying populations. We investigate its asymptotic distribution in a general framework characterized by the data dimension $p$, sample size $n$, and regularly varying index $\alpha$. In particular, we identify a phase transition phenomenon in the asymptotic behavior. For light-tailed populations ($\alpha > 3$), we revisit the $\alpha$-free asymptotic distribution but relax the constraint on the ratio of $p/n$. For heavy-tailed populations ($\alpha < 3$), we derive a new asymptotic normal distribution whose variance explicitly depends on $\alpha$. We also propose a consistent estimator for the asymptotic variance such that the standardized Schott's test statistic remains applicable for unknown location parameters and all $\alpha > 0$.

报告人介绍： 王成，上海交通⼤学数学科学学院长聘副教授，博士生导师。2013年博士毕业于中国科学技术⼤学，主要研究⽅向为随机矩阵理论及应⽤、⾼维数据分析等。在统计领域核⼼期刊Statistica Sinica, Science China Mathematics等发表学术论⽂三十余篇。先后主持国家⾃然科学基⾦青年基金、面上项目2项、上海市科研项⽬2项，参与国家⾃然科学基⾦重大项目和重点项⽬。曾获得过中科院院⻓特别奖，上海交大教书育人三等奖等荣誉。