False discovery rate approach to dynamic change detection

Abstract

In multiple data stream surveillance, the rapid and sequential identification of individuals whose behavior deviates from the norm has become particularly important. In such applications, the state of a stream can alternate, possibly multiple times, between a null state and an alternative state. To balance the ability to detect two types of changes, that is, a change from the null to the alternative and back to the null, we propose a new multiple testing procedure based on a penalized version of the generalized likelihood ratio test statistics for change detection. The false discovery rate (FDR) at each time point is shown to be controlled under some mild conditions on the dependence structure of data streams. A data-driven approach is developed for selection of the penalization parameter. Its advantage is demonstrated via simulation and a data example.