A unified data‐adaptive framework for high dimensional change point detection

Bin Liu, Cheng Zhou, Xinsheng Zhang and Yufeng Liu

Journal of the Royal Statistical Society Series B, 2020, vol. 82, issue 4, 933-963

Abstract: In recent years, change point detection for a 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. the 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 that are suitable for a large class of parameters, and also adaptive to various alternative scenarios. In particular, by generalizing the classical cumulative sum statistic, we construct the U‐statistic‐based cumulative sum 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 on the basis of 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 co‐ordinates 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 to be much larger than the sample size n. An R package called AdaptiveCpt is developed to implement our algorithms. Extensive simulation studies provide further support for our theory. An application to a comparative genomic hybridization data set also demonstrates the usefulness of our proposed methods.

Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://doi.org/10.1111/rssb.12375

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:82:y:2020:i:4:p:933-963

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().