报告名称：Robust estimation of high dimensional linear regression with change point.

报告人：王兆军 教授 南开大学

报告时间：2025年12月17日 下午3:30--5:00

腾讯会议：124-758-226

校内联系人：李聪 [email protected]

报告摘要：The identification of changes in linear models is a fundamental problem encountered in various applications. Traditional methods often encounter difficulties when attempting to identify changepoints in the presence of heavy-tailed distribution. This paper focuses on the study of high-dimensional linear models with multiple structural changes in the presence of heavy-tailed errors, especially for those errors without moment conditions. We first propose a robust method that simultaneously estimates regression coefficient and changepoint by incorporating ℓ1 norm penalized Wilcoxon rank loss minimization for single changepoint estimation. Furthermore, we extend it to multiple changepoints estimation based on a novel two-step moving window mechanism that combines fast coarse grid screening and an efficient refinement. Our method exhibits robustness against heavy-tailed random errors while maintaining high efficiency for normal random errors. Theoretically, we establish non-asymptotic error bounds with a near-oracle rate for the estimates of both the coefficient and the changepoint under weak conditions on the random error distribution. Numerical results provide evidence for the validity and effectiveness of the proposed approach.

个人简介：

王兆军，南开大学杰出教授，教育部长江学者特聘教授，现任南开大学统计与数据科学学院执行院长，国务院统计学科评议组成员、中国工业与应用数学学会副理事长、中国工业统计教学研究会副会长、中国概率统计学会副理事长、全国统计教材编写委员会委员，曾任国家统计专家咨询委员会委员、国家自然科学基金委天元基金领导小组成员、中国现场统计研究会副理事长、天津市现场统计研究会理事长，天津工业与应用数学学会理事长，曾获国务院政府特贴、全国百篇优博指导教师、教育部自然科学二等奖及天津市自然科学一等奖。研究兴趣包括试验设计、在线监控、变点检测、高维统计推断、统计学习等，在包括国际统计顶刊Annals of Statistics, Journal of American Statistical Association, Biometrika等杂志上发表论文近百篇。