A min-max test for detecting a transient signal

Abstract

Page's (1954) test is optimal for detecting a permanent change in the distribution, in the sense that it minimizes the average delay to detection given an average distance between false alarms. When used to detect transient signals, however, it in fact becomes the generalized likelihood ratio test (GLRT). Since a GLRT is in almost all cases ad hoc, Page's test used as such cannot be said to be optimal in any explicit sense. The subject of this paper is the development of the min-max test for the detection of a transient.