報(bào) 告 人：劉彬 副教授

報(bào)告題目：A General U-Statistic Framework for High-DimensionalMultiple Change-Point Analysis

報(bào)告時(shí)間：2025年7月4日（周五）上午10:00

報(bào)告地點(diǎn)：騰訊會(huì)議 600-690-265

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

      劉彬，復(fù)旦大學(xué)管理學(xué)院統(tǒng)計(jì)與數(shù)據(jù)科學(xué)系副教授。劉彬2013年本科畢業(yè)于山東大學(xué)，2013-2019年在復(fù)旦大學(xué)管理學(xué)院獲概率論與數(shù)理統(tǒng)計(jì)專(zhuān)業(yè)理學(xué)博士學(xué)位，師從張新生教授。2019-2020年在香港中文大學(xué)統(tǒng)計(jì)系進(jìn)行博士后研究。先后主持國(guó)自然青年基金和面上項(xiàng)目，參與國(guó)自然重點(diǎn)項(xiàng)目。他的主要研究方向?yàn)楦呔S統(tǒng)計(jì)推斷，變點(diǎn)分析，數(shù)據(jù)趨動(dòng)檢驗(yàn)，穩(wěn)健方法以及機(jī)器學(xué)習(xí)等，并在 JRSSB，JASA，JMLR，Statistica Sinica, JMVA等統(tǒng)計(jì)期刊發(fā)表多篇論文。

報(bào)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.