论文标题
依赖数据流的联合顺序检测和隔离
Joint Sequential Detection and Isolation for Dependent Data Streams
论文作者
论文摘要
在多个（不一定是独立的数据流）的背景下，考虑了联合顺序检测和隔离的问题。提出了一个多重测试框架，其中每个假设对应于数据流的不同子集，样本大小是观察值的停止时间，并且四种错误的概率被控制在不同的用户指定级别以下。这些误差中有两个反映了公式的检测成分，而另外两个隔离组件。当误差概率为0时，最佳预期样本量的特征是一阶渐近近似。不同的渐近方案，表达了对检测和隔离任务的不同优先级的不同优先级。提出了一个新颖的，多功能的测试程序系列，其中为每个假设计算两个不同的统计数据，一个针对检测任务，另一个针对隔离任务。在不同的设置下，该家族的测试（各种计算复杂性）在不同的设置下均无最佳。一般理论应用于异常的检测和隔离，不一定是独立的数据流，以及对未知依赖性结构的检测和隔离。
The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the formulation, whereas the other two the isolation component. The optimal expected sample size is characterized to a first-order asymptotic approximation as the error probabilities go to 0. Different asymptotic regimes, expressing different prioritizations of the detection and isolation tasks, are considered. A novel, versatile family of testing procedures is proposed, in which two distinct, in general, statistics are computed for each hypothesis, one addressing the detection task and the other the isolation task. Tests in this family, of various computational complexities, are shown to be asymptotically optimal under different setups. The general theory is applied to the detection and isolation of anomalous, not necessarily independent, data streams, as well as to the detection and isolation of an unknown dependence structure.
