Sequential common change detection, isolation, and estimation in multiple compound Poisson processes

Abstract

We explore and compare the detection of changes in both the arrival rate and jump size mean and estimation of change-time after detection within a compound Poisson process by using generalized CUSUM and Shiryayev–Roberts (S–R) procedures. Average in-control and out-of control lengths are derived as well as the limiting distribution of the generalized CUSUM processes. The asymptotic bias of change time estimation is also derived. To detect a common change in multiple compound Poisson processes where change only occurs in a portion of panels, a unified algorithm is proposed that employs the sum of S–R processes to detect a common change, uses individual CUSUM processes to isolate the changed panels with False Discovery Rate (FDR) control, and then estimate the common change time as the median of the estimates obtained from the isolated channels. To illustrate the approach, we apply it to mining disaster data in the USA.