• ## 统计与管理学院2018年学术报告第10期

【主 题】 Change-point Analysis for Banach-Valued Sequences

【报告人】 王学钦 教授

中山大学

【时 间】 2018年03月16日（星期五）14:00-15:00

【地 点】 上海财经大学统计与管理学院大楼1208会议室

摘 要】In this paper, we extend a measure of divergence between two distributions: Ball divergence, to a new one: $\alpha$-Ball divergence. With this new notion, we propose its sample statistic which can be used to test whether two weakly dependent sequences of Banach-valued random vectors have the same distribution. The properties of $\alpha$-Ball divergence and its sample statistic, as Ball divergence has, are inspected and shown to hold for random sequences which are functionals of some absolutely regular sequences. We further apply the sample statistic to change-point problems for a sequence of weakly dependent Banach-valued observations with multiple possible change-points. Our procedure does not require any assumptions on special change-point type. It could detect the number of change-points as well as their locations. We also prove the consistency of the estimated change-point locations. Extensive simulation studies and analyses of two interesting real datasets about wind direction and bitcoin price illustrate that our procedure has considerable advantages over other existing competitors, especially when observations are non-Euclidean or there are distributional changes in the variance.

嘉宾简介】王学钦，中山大学数学学院和中山医学院双聘教授，博士生导师，中山大学华南统计科学研究中心执行主任，国家优秀青年基金获得者，教育部新世纪人才，教育部统计专业教指委委员。研究领域：非参多元统计学、统计学习和精准医学。