A Unified Data-adaptive Framework for High Dimensional Change Point Detection

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 (e.g. mean or covariance) or a particular alternative pattern (sparse or dense), but not for both scenarios simultaneously. To overcome this limitation, we provide a general framework for developing tests suitable for a large class of parameters, and also adaptive to various alternative scenarios. In particular, by generalizing the classical cumulative sum (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. With flexible dependence structure across coordinates and 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.  [This is joint work with Bin Liu, Cheng Zhou and Yufeng Liu]