Open Access
August 2019 High-dimensional change-point detection under sparse alternatives
Farida Enikeeva, Zaid Harchaoui
Ann. Statist. 47(4): 2051-2079 (August 2019). DOI: 10.1214/18-AOS1740


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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Farida Enikeeva. Zaid Harchaoui. "High-dimensional change-point detection under sparse alternatives." Ann. Statist. 47 (4) 2051 - 2079, August 2019.


Received: 1 February 2014; Revised: 1 March 2018; Published: August 2019
First available in Project Euclid: 21 May 2019

zbMATH: 07082279
MathSciNet: MR3953444
Digital Object Identifier: 10.1214/18-AOS1740

Primary: 62G10 , 62H15
Secondary: 60G35

Keywords: Change-point problem , High-dimensional data , Minimax optimality , Sparsity

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 4 • August 2019
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