From Central Limit Theorem to Self-Normalized High Dimensional Gaussian Approximation


报告专家:邵启满(南方科技大学统计与数据科学系)

报告时间:2024年6月13日(星期四)下午16:00-17:00

报告地点:国家天元数学西南中心516报告厅

报告摘要:The normalizing coefficients are usually deterministic in the classical limit theory, however, for most commonly used  statistics such as  the Student t-statistic, the standardized coefficients are typically random, or  self-normalized. Last two decades has witnessed significant progress on self-normalized limit theory in probability and statistics. In contrast with the classical limit theorems, self-normalized  limit theorems, especially Cramér type moderate deviation theorems, require much less moment assumptions. In this talk, we shall review the development from the central limit theorem to the self-normalized high dimensional Gaussian approximation and show how the self-normalization tames a wild population  in a heavy-tailed world.

专家简介:邵启满,南方科技大学统计与数据科学系讲席教授。他主要研究概率统计基础理论,系统深入地发展了自正则化极限理论,建立了自正则化大偏差、中偏差定理,发展完善了正态与非正态逼近的Stein方法,建立了随机浓度不等式和确定极限分布的基本方法,给出了一系列重要的矩和概率不等式及强逼近弱收敛等基础性工作。他曾应邀在国际数学家大会作45分钟报告,曾获国家自然科学二等奖(第一完成人)及美国数理统计学会Medallion奖章,现任《Annals of Applied Probability 》联合主编, 《Science China Mathematics》副主编,曾任概率统计顶级国际期刊《Annals of Statistics》等编委。

邀请人:王宝富

0530-王宝富-邵启满.jpg