报告人：王学钦(中国科学技术大学管理学院讲席教授)
主持人：李仲飞
讲座时间：2022年12月19日（周一）下午14:30-16:30
腾讯会议：488-928-831
讲座介绍：
       Change is the only constant in reality. Detecting changes and making statistical inferences based on local stationarity is vital in a stochastic data sequence. As in analyzing network and shape data, the events that change are not always characterized as objects in a Euclidean space. There is a growing importance and urgency to analyze the dynamics in the time series of data objects in a non-Euclidean space. However, existing methods are predominantly developed for Euclidean data by using the characteristics of Euclidean spaces. There is little research on whether existing methods are useful for non-Euclidean sequences. Through simulation studies of manifold-valued sequences and dynamic network sequences, we demonstrate that existing methods do not perform well in detecting dynamical changes of probability measures(regimes) in non-Euclidean sequences. Thus, it is imperative to develop methods to detect dynamical regime changes in non-Euclidean sequences effectively. To this end, we introduce a nonparametric and hierarchical approach that identifies time points at which an abrupt change occurs in the probability measure of non-Euclidean data in metric spaces. Our approach is also practical for Euclidean data. Using the metric, we define a metric based binary partition function that reaches the maximum at a change point. We not only show that our approach can estimate the number of change-points and detect their locations consistently but also provide that the convergence rate of the estimated change points is OP (1/T), which is optimal. Extensive simulation studies and analysis of a real dataset demonstrate that our method has considerable advantages over state-of-the-art methods, especially when data are non-Euclidean or covariance structures change over time.
报告人介绍：
      王学钦，中国科学技术大学管理学院讲席教授，2003年毕业于纽约州立大学宾汉姆顿分校，教育部高层次人才入选者。现担任教育部高等学校统计学类专业教学指导委员会委员、中国现场统计研究会副理事长、统计学国际期刊JASA等的Associate Editor、高等教育出版社Lecture Notes: Data Science, Statistics and Probability系列丛书的副主编。