ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM

We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is th...

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Veröffentlicht in:The Annals of applied probability 2015-12, Vol.25 (6), p.3405-3433
Hauptverfasser: Zhang, Hongzhong, Rodosthenous, Neofytos, Hadjiliadis, Olympia
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creator Zhang, Hongzhong
Rodosthenous, Neofytos
Hadjiliadis, Olympia
description We study a Wiener disorder problem of detecting the minimum of N change-points in N observation channels coupled by correlated noises. It is assumed that the observations in each dimension can have different strengths and that the change-points may differ from channel to channel. The objective is the quickest detection of the minimum of the N change-points. We adopt a min–max approach and consider an extended Lorden's criterion, which is minimized subject to a constraint on the mean time to the first false alarm. It is seen that, under partial information of the post-change drifts and a general nonsingular stochastic correlation structure in the noises, the minimum of N cumulative sums (CUSUM) stopping rules is asymptotically optimal as the mean time to the first false alarm increases without bound. We further discuss applications of this result with emphasis on its implications to the efficiency of the decentralized versus the centralized systems of observations which arise in engineering.
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subjects 60G40
60K35
62C20
62L10
62L15
Asymptotic methods
correlated noise
Correlation analysis
CUSUM
Noise
quickest detection
Stochastic models
Wiener disorder problem
title ROBUSTNESS OF THE N-CUSUM STOPPING RULE IN A WIENER DISORDER PROBLEM
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