报告题目 (Title)：CLT for high-dimensional R^2 statistics under a general independent components model (一般独立成分模型下高维R^2统计量的CLT)

报告人 (Speaker)：李卫明 长聘副教授（上海财经大学）

报告时间 (Time)：2022年9月4日 (周日) 13:30

报告地点 (Place)：腾讯会议（会议号：385-558-280）

邀请人(Inviter)：张阳春

主办部门：理学院数学系

报告摘要：This paper establishes a central limit theorem (CLT) for R^2 statistics in a moderately high-dimensional asymptotic framework. The underlying population accommodates a general independent components model, by virtue of which our result unifies the two CLTs proposed separately in Zheng et al. (2014) and Guo and Cheng (2021). Beyond this, the new CLT demonstrates a non-negligible impact of kurtosis of the latent independent components on the fluctuation of R^2 statistics. As an application, a novel confidence interval is constructed for the coefficient of multiple correlation in a high-dimensional linear regression.