报 告 人：刘彬 副教授
报告题目：A General U-Statistic Framework for High-DimensionalMultiple Change-Point Analysis
报告时间：2025年7月4日（周五）上午10:00
报告地点：腾讯会议 600-690-265
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
刘彬，复旦大学管理学院统计与数据科学系副教授。刘彬2013年本科毕业于山东大学，2013-2019年在复旦大学管理学院获概率论与数理统计专业理学博士学位，师从张新生教授。2019-2020年在香港中文大学统计系进行博士后研究。先后主持国自然青年基金和面上项目，参与国自然重点项目。他的主要研究方向为高维统计推断，变点分析，数据趋动检验，稳健方法以及机器学习等，并在 JRSSB，JASA，JMLR，Statistica Sinica, JMVA等统计期刊发表多篇论文。
报告摘要：
High-dimensional change-point analysis is essential in modern statistical inference. However, existing methods are often designed either for specific parameters (e.g., mean or variance) or for particular tasks (e.g., testing or estimation), making them difficult to generalize. Moreover, they typically rely onrestrictive distributional assumptions, limiting their robustness to heavy-tailed data. We propose a unified framework for testing, estimating, and inferring multiple change points in high-dimensional data. Our approach leverages a two-sample U-statistic within a moving window, allowing flexible kernel function selection to accommodate structural changes in general parameters. For testing, we develop an L∞-norm-based statistic with a high-dimensional multiplier bootstrap, achieving minimax-optimal power under sparse alternatives. For estimation, we construct an initial estimator for change-point number and locations and refine it using the U-statistic Projection Refinement Algorithm(U-PRA), attaining minimax-optimal localization rates. We further derive the asymptotic distribution of refined estimators, enabling valid confidence interval construction. Extensive numerical experiments demonstrate the superior performance of our method across various settings, including heavy-tailed distributions. Applications to genomic copy number variation and financial time series data highlight its practical utility.