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Robustness of the \(N\)-CUSUM stopping rule in a Wiener disorder problem. (English) Zbl 1328.62500
Summary: 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.

MSC:
62L10 Sequential statistical analysis
60K35 Interacting random processes; statistical mechanics type models; percolation theory
62L15 Optimal stopping in statistics
62C20 Minimax procedures in statistical decision theory
60G40 Stopping times; optimal stopping problems; gambling theory
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