${N}$ - CUSUM停止规则在Wiener无序问题中的鲁棒性
Robustness of the ${N}$-CUSUM stopping rule in a Wiener disorder problem
摘要：
研究了在相关噪声耦合的$N$观测通道中检测$N$变点最小值的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。目标是最快地检测$N$变化点的最小值。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。结果表明，在噪声中具有一般非奇异随机相关结构和变化后漂移的部分信息下，当到达第一个虚警的平均时间无限制地增加时，$N$累积和停止规则的最小值是渐近最优的.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。
英文摘要：
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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