Robustness of the N-CUSUM stopping rule in a Wiener disorder problem
Robustness of the N-CUSUM stopping rule in a Wiener disorder problem
复制标题
维纳无序问题中 N-CUSUM 停止规则的稳健性
DOI：
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发表时间：
2014
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影响因子：
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通讯作者：
O. Hadjiliadis
中科院分区：
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作者：
Hongzhong Zhang;Neofytos Rodosthenous;O. Hadjiliadis
本文研究了在N个观测通道中检测N个最小变点的Wiener无序问题。假设每个维度中的观测值可以具有不同的强度，并且变点可以因通道而异。我们的目标是最快的检测最小的$N$变点。我们采用最小-最大的方法，并考虑扩展的Lorden的标准，这是最小化的约束的平均时间到第一个虚警。可以看出，部分信息下的变化后漂移和一般的非奇异随机相关结构的噪声，最小的$N$累积和（Cumulative Sums）停止规则是渐近最优的平均时间的第一个虚警增加没有限制。我们进一步讨论了这一结果的应用，强调其影响的效率，分散与集中系统的意见，出现在工程。
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.