A variable threshold page procedure for detection of transient signals

When employed to detect a transient change between known independent identically distributed populations, Page's test is easy to implement and provides reliable performance. However, its application to unknown transient changes is less clear. A Page test can be thought of as a repeated sequential test, and here we propose that each sequential test use a time-varying threshold. The idea is that short signals are detected quickly before post-termination data has a chance to refute them; and that evidence for a long signal is allowed to build, rather than being summarily discarded too early. Simulations results show that the performance of the proposed scheme comes close to tracing the "envelope" of fixed-style Page tests.