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2018 Change-point detection in high-dimensional covariance structure
Valeriy Avanesov, Nazar Buzun
Electron. J. Statist. 12(2): 3254-3294 (2018). DOI: 10.1214/18-EJS1484

Abstract

In this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process – a problem, which has applications in many areas e.g., neuroimaging and finance. The developed approach is essentially a testing procedure involving a choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. Theoretical study features a result providing guaranties for break detection. All the theoretical results are established in a high-dimensional setting (dimensionality $p\gg n$). Multiscale nature of the approach allows for a trade-off between sensitivity of break detection and localization. The approach can be naturally employed in an on-line setting. Simulation study demonstrates that the approach matches the nominal level of false alarm probability and exhibits high power, outperforming a recent approach.

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Valeriy Avanesov. Nazar Buzun. "Change-point detection in high-dimensional covariance structure." Electron. J. Statist. 12 (2) 3254 - 3294, 2018. https://doi.org/10.1214/18-EJS1484

Information

Received: 1 May 2017; Published: 2018
First available in Project Euclid: 5 October 2018

zbMATH: 06970004
MathSciNet: MR3861282
Digital Object Identifier: 10.1214/18-EJS1484

Subjects:
Primary: 62H15 , 62M10
Secondary: 62P10 , 91B84

Keywords: bootstrap , critical value , multiscale , precision matrix , structural change

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Vol.12 • No. 2 • 2018
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