An Optimal Retrospective Change Point Detection Policy

Since the middle of the twentieth century, the problem of making inferences about the point in a surveyed series of observations at which the underlying distribution changes has been extensively addressed in the economics, biostatistics and statistics literature. Cumulative sum-type statistics have commonly been thought to play a central role in non-sequential change point detections. Alternatively, we present and examine an approach based on the Shiryayev-Roberts scheme. We show that retrospective change point detection policies based on Shiryayev-Roberts statistics are non-asymptotically optimal in the context of most powerful testing.