光华讲坛——社会名流与企业家论坛第6383期
主题：Change point estimation for high-dimensional data
主讲人：伊利诺伊大学香槟分校 邵晓峰教授
主持人：统计学院 常晋源教授
时间：1月6日 9:30-10:30
举办地点：腾讯会议，会议ID：811-787-591
主办单位：数据科学与商业智能联合实验室 统计学院 科研处
主讲人简介：
Dr. Shao is Professor of Statistics and PhD program director, at the Department of Statistics, University of Illinois at Urbana-Champaign (UIUC). He received his PhD in Statistics from University of Chicago in 2006 and has been on the UIUC faculty since then. Dr. Shao's research interests include time series analysis, high-dimensional data analysis, functional data analysis, change-point analysis, resampling methods and asymptotic theory. He is an elected ASA and IMS fellow.
邵晓峰，美国伊利诺伊大学香槟分校统计学教授，博士生项目主任。他于2006年获得了芝加哥大学的统计学博士学位，此后一直在美国伊利诺伊大学香槟分校任教。主要研究方向为时间序列分析、高维数据分析、函数型数据分析、变点分析、重采样方法和渐进理论。他是当选的ASA和IMS成员。
内容简介：
In this talk, I will present some recent work on change point estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its convergence rate and asymptotic distribution after suitable centering and normalization are obtained under mild assumptions. Our estimator turns out to have better efficiency as compared to the least squares based counterpart in the literature. Based on the asymptotic theory, we construct a confidence interval by plugging in consistent estimates of several quantities in the normalization. We also provide a bootstrap-based confidence interval and state its asymptotic validity under suitable conditions. Through simulation studies, we demonstrate favorable finite sample performance of the new change point location estimator as compared to its least squares based counterpart, and our bootstrap-based confidence intervals, as compared to several existing competitors.
本期讲座将介绍最近在独立高维数据均值中变点位置估计和推断方面的一些工作。本文的变点位置估计量最大化了一个新的基于U统计量的目标函数，并且在温和的假设下，通过适当的居中和归一化后，可得到它的收敛速度和渐近分布。与文献中基于最小二乘法的估计相比，本文的估计具有更好的效率。基于渐近理论，本文通过在归一化中插入几个量的一致估计来构建置信区间。本文还提供了一个基于自举法的置信区间，并说明了其在适当条件下的渐近有效性。通过模拟研究，本文证明了与基于最小二乘法的估计量相比，新的变点位置估计量具有更好的有限样本性能，与现有的其他方法相比，基于自举法的置信区间也具有更好的性能。
