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2018 Change detection via affine and quadratic detectors
Yang Cao, Arkadi Nemirovski, Yao Xie, Vincent Guigues, Anatoli Juditsky
Electron. J. Statist. 12(1): 1-57 (2018). DOI: 10.1214/17-EJS1373

Abstract

The goal of the paper is to develop a specific application of the convex optimization based hypothesis testing techniques developed in A. Juditsky, A. Nemirovski, “Hypothesis testing via affine detectors,” Electronic Journal of Statistics 10:2204–2242, 2016. Namely, we consider the Change Detection problem as follows: observing one by one noisy observations of outputs of a discrete-time linear dynamical system, we intend to decide, in a sequential fashion, on the null hypothesis that the input to the system is a nuisance, vs. the alternative that the input is a “nontrivial signal,” with both the nuisances and the nontrivial signals modeled as inputs belonging to finite unions of some given convex sets. Assuming the observation noises are zero mean sub-Gaussian, we develop “computation-friendly” sequential decision rules and demonstrate that in our context these rules are provably near-optimal.

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Yang Cao. Arkadi Nemirovski. Yao Xie. Vincent Guigues. Anatoli Juditsky. "Change detection via affine and quadratic detectors." Electron. J. Statist. 12 (1) 1 - 57, 2018. https://doi.org/10.1214/17-EJS1373

Information

Received: 1 February 2017; Published: 2018
First available in Project Euclid: 3 January 2018

zbMATH: 06825052
MathSciNet: MR3743736
Digital Object Identifier: 10.1214/17-EJS1373

Subjects:
Primary: 62C20
Secondary: 90C22

Keywords: change-point detection , semi-definite program

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Vol.12 • No. 1 • 2018
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