報 告 人：劉彬 副教授
報告題目：A General U-Statistic Framework for High-DimensionalMultiple Change-Point Analysis
報告時間：2025年7月4日（周五）上午10:00
報告地點：騰訊會議 600-690-265
主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術研究院
報告人簡介：
劉彬，復旦大學管理學院統(tǒng)計與數(shù)據科學系副教授。劉彬2013年本科畢業(yè)于山東大學，2013-2019年在復旦大學管理學院獲概率論與數(shù)理統(tǒng)計專業(yè)理學博士學位，師從張新生教授。2019-2020年在香港中文大學統(tǒng)計系進行博士后研究。先后主持國自然青年基金和面上項目，參與國自然重點項目。他的主要研究方向為高維統(tǒng)計推斷，變點分析，數(shù)據趨動檢驗，穩(wěn)健方法以及機器學習等，并在 JRSSB，JASA，JMLR，Statistica Sinica, JMVA等統(tǒng)計期刊發(fā)表多篇論文。
報告摘要：
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.