时 间：2019年6月17日(周一)下午13:30-14:30
地 点：中北校区理科大楼A1514会议室
题 目：A Unified Data-adaptive Framework for High Dimensional Change Point Detection
报告人：张新生 复旦大学 教授
摘 要：
In recent years, change point detection for high dimensional data sequence has become increasingly important in many scientific fields such as biology and finance. The existing literature develops a variety of methods designed for either a specified parameter or a particular alternative pattern, but not for both scenarios simultaneously. We provide a general framework for developing tests suitable for a large class of parameters, and also adaptive to various alternative scenarios. In particularly, by generalizing the classical CUSUM statistic, we construct U-statistic based the CUSUM matrix C. Two cases corresponding to common or different change point locations across the components are considered. We then propose two types of individual test statistics by aggregating C based on the adjusted Lp-norm with p ∈ {1, · · · , ∞}. Combining the corresponding individual tests, we construct two types of data-adaptive tests for the two cases, which are both powerful under various alternative patterns. A multiplier bootstrap method is introduced for approximating the proposed test statistics’ limiting distributions. Under mild moment conditions, we show the optimality of our methods theoretically in terms of size and power by allowing the dimension d and the number of parameters q being much larger than the sample size n. Extensive simulation studies provide further support for our theory. An application to the S&P 100 dataset also demonstrates the usefulness of our proposed methods.
报告人简介：
张新生，复旦大学统计系教授、博士生导师、系主任。上海市数学会第十一届理事会常务理事、中国现场统计研究会生存分析分会副理事长、教育部高等学校数学与统计学教学指导委员会统计学专业教学指导分委员会委员等职务。