A detection optimal min-max test for transient signals

Page's (1954) test is optimal for detecting a permanent change in distribution, in the sense that it minimizes the worst case 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. This article discusses the development of the min-max test, via the new ideas of Baygun and Hero (see ibid., vol.41, p.688-703, 1995) for the detection of a transient.