Speaker: Prof. Lihu Xu, University of Macau and Harvard University 

Title: Robust heavy tailed statistical estimations

Abstract: 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 $\beta$-th moment with $\beta \in (1,2]$. 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 $\beta \uparrow 2$. 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 data are heavy tailed. We will also consider a medium of mean estimator via DNN-based GAN. 

Short Bio: Dr. Lihu Xu received his PhD at Imperial College in 2008, and is currently an associate professor in the Department of Mathematics at the University of Macau. From January 2024  to July 2024, Dr. Lihu Xu is a visiting faculty in the Department of Statistics at Harvard University. His research interests lie in applied stochastic analysis, high dimensional statistics, and stochastic algorithms related to machine learning. He has published more than 50 papers on journals such as  Annals of Applied Probability, Annals of Statistics, Journal of Machine Learning Research, Probability Theory and Related Fields, Mathematics of Operations Research, etc.