报告题目： A Unified Data-adaptive Framework for High Dimensional Change Point Detection

报 告 人： 张新生教授（复旦大学统计学系）

报告时间：2018年11月17日16:00-17:00

报告地点：知新楼B-1238

报告摘要：

In recent years,change point detection for high dimensional data sequence has becomeincreasingly important in many scientific fields such as biology and finance.The existing literature develops a variety of methods designed for either aspecified parameter (e.g. mean or covariance) or a particular alternativepattern (sparse or dense), but not for both scenarios simultaneously. Toovercome this limitation, we provide a general framework for developing testssuitable for a large class of parameters, and also adaptive to variousalternative scenarios. In particular, by generalizing the classical cumulativesum (CUSUM) statistic, we construct U-statistic based the CUSUM matrix C. Two casescorresponding to common or different change point locations across thecomponents are considered. We then propose two types of individual teststatistics by aggregating C based on the adjusted Lp-norm with p ∈ {1, · · · ,∞}. Combining the corresponding individual tests, we construct two types ofdata-adaptive tests for the two cases, which are both powerful under variousalternative patterns. A multiplier bootstrap method is introduced forapproximating the proposed test statistics’ limiting distributions. Withflexible dependence structure across coordinates and mild moment conditions, weshow the optimality of our methods theoretically in terms of size and power byallowing the dimension d and the number of parameters q being much larger thanthe sample size n. Extensive simulation studies provide further support for ourtheory. An application to the S&P 100 dataset also demonstrates theusefulness of our proposed methods. [This is joint work with Bin Liu, Cheng Zhou and Yufeng Liu]

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