论文标题
顺序更改诊断和自适应矩阵库
Sequential Change Diagnosis Revisited and the Adaptive Matrix CuSum
论文作者
论文摘要
考虑了顺序变化诊断的问题，在线获得观测值，在分布中发生突然的变化，目标是快速检测变化并准确确定后变化后分布，同时控制错误的警报率。假定对变更后制度的一组有限的替代方案，但没有假定未知的更改点的事先信息。为此问题提出的许多算法的缺点是隐式使用前更改数据来确定后变化分布。鉴于没有错误的警报，这可能会导致很大的有条件识别概率，除非此次更改在监视开始后不久发生。提出了一种新颖的递归算法，并证明可以解决此问题，而无需使用其他调整参数，而不会牺牲洛尔登意义上最严重的延迟。对一般性变化诊断程序的一般家族进行了理论分析，该程序支持拟议的算法并修改某些最新结果。此外，提出了一种新颖的，全面的方法，用于设计和评估顺序变化诊断算法。通过模拟研究说明了这种方法，其中将现有程序与提议的研究进行了比较。
The problem of sequential change diagnosis is considered, where observations are obtained on-line, an abrupt change occurs in their distribution, and the goal is to quickly detect the change and accurately identify the post-change distribution, while controlling the false alarm rate. A finite set of alternatives is postulated for the post-change regime, but no prior information is assumed for the unknown change-point. A drawback of many algorithms that have been proposed for this problem is the implicit use of pre-change data for determining the post-change distribution. This can lead to very large conditional probabilities of misidentification, given that there was no false alarm, unless the change occurs soon after monitoring begins. A novel, recursive algorithm is proposed and shown to resolve this issue without the use of additional tuning parameters and without sacrificing control of the worst-case delay in Lorden's sense. A theoretical analysis is conducted for a general family of sequential change diagnosis procedures, which supports the proposed algorithm and revises certain state-of-the-art results. Additionally, a novel, comprehensive method is proposed for the design and evaluation of sequential change diagnosis algorithms. This method is illustrated with simulation studies, where existing procedures are compared to the proposed.
