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
VIDEOS