报告人：徐礼虎(澳门大学珠海研究院)

报告题目：Catoni type robust estimation for heavy tailed distribution

报告摘要：We extend the well known Catoni's robust estimator, which was originally designed to estimate the mean of the data with finite second moment, to the situation in which the data are heavy tailed and only have finite $\alpha$-th moment with $\alpha \in (1,2]$. Inspired by the generalized Taylor expansion developed in the Stein's method for stable approximation, we propose a new influence truncation function and obtain a mean estimator for heavy tailed data. This estimator enjoys the nice properties of Caton's estimator and recovers his classical result as $\alpha \uparrow 2$. Based on the new influence function, we put forward a general robust estimation framework, which covers classical statistical estimations such as quantile regression, generalized linear models, elastic net, etc. Simulations confirm that our robust estimation outperforms other related estimations when the samples are heavy tailed.

报告时间：2024年8月2日（星期五）15:30-16:30

报告地点：科技楼南楼711室

邀请人：吴付科

报告人简介：澳门大学副教授，博士生导师。2001年毕业于山东大学，获学士学位；2004年毕业于北京大学，获硕士学位；2008年毕业于英国帝国理工学院，获博士学位。主要研究方向：随机分析、极限理论。在国内外学术刊物Annals of Statistics, Probability Theory and Related Fields, Bernoulli等上发表学术论文多篇。