報告人：徐禮虎(澳門大學珠海研究院)

報告題目：Catoni type robust estimation for heavy tailed distribution

報告摘要：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.

報告時間：2024年8月2日（星期五）15:30-16:30

報告地點：科技樓南樓711室

邀請人：吳付科

報告人簡介：澳門大學副教授，博士生導師。2001年畢業于山東大學，獲學士學位；2004年畢業于北京大學，獲碩士學位；2008年畢業于英國帝國理工學院，獲博士學位。主要研究方向：随機分析、極限理論。在國内外學術刊物Annals of Statistics, Probability Theory and Related Fields, Bernoulli等上發表學術論文多篇。