HIGH-DIMENSIONAL CHANGE-POINT DETECTION UNDER SPARSE ALTERNATIVES
成果类型：
Article
署名作者：
Enikeeva, Farida; Harchaoui, Zaid
署名单位：
Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; University of Washington; University of Washington Seattle
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/18-AOS1740
发表日期：
2019
页码：
2051-2079
关键词：
摘要：
We consider the problem of detecting a change in mean in a sequence of high-dimensional Gaussian vectors. The change in mean may be occurring simultaneously in an unknown subset components. We propose a hypothesis test to detect the presence of a change-point and establish the detection boundary in different regimes under the assumption that the dimension tends to infinity and the length of the sequence grows with the dimension. A remarkable feature of the proposed test is that it does not require any knowledge of the subset of components in which the change in mean is occurring and yet automatically adapts to yield optimal rates of convergence over a wide range of statistical regimes.
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