Abstract

Quick detection of common changes is critical in sequential monitoring of multi-stream data where a common change is referred as a change that only occurs in a portion of panels. After a common change is detected by using a SR-SUM procedure, we compare the CUSUM and EWMA methods in terms of FDR and FNR after a common change is detected. The BH-type procedure is used for both CUSUM processes and EWMA processes at the detection time to isolate the changed panels with the control of FDR (False Discovery Rate). The numerical results show that the FNR for the CUSUM method is smaller than that for the EWMA method. Also the CUSUM method has the advantage that the common change point is conveniently estimated after isolation. To reduce the FNR, the tightened FDR control procedure is considered by using the estimated number of changed panels. Further, the estimated number of changed panels can also be used to identify whether the alarm is true or false.

摘要

快速检测常见变化对于顺序监控多流数据至关重要，其中常见变化被称为仅发生在部分面板中的变化。在使用 SR-SUM 过程检测到共同变化后，我们在检测到共同变化后在 FDR 和 FNR 方面比较 CUSUM 和 EWMA 方法。BH 型程序在检测时用于 CUSUM 过程和 EWMA 过程，以在 FDR（错误发现率）的控制下隔离更改的面板。数值结果表明，CUSUM 方法的 FNR 小于 EWMA 方法的 FNR。此外，CUSUM 方法的优点是可以方便地在隔离后估计共同变化点。为了减少 FNR，通过使用估计的更换面板数量来考虑收紧的 FDR 控制程序。更远，