SUBOPTIMAL PROPERTIES OF PAGE'S CUSUM AND SHIRYAYEV-ROBERTS PROCEDURES IN CHANGE-POINT PROBLEMS WITH DEPENDENT OBSERVATIONS

We construct a simple counterexample to the conjectures of Pollak (1985) and Yakir, Krieger and Pollak (1999), which state that Page's CUSUM procedure and the Shiryayev-Roberts procedure are asymptotically minimax optimal for de- pendent observations. Moreover, our example shows that the close relationship between open-ended tests and change-point detection procedures no longer holds for dependent observations. As a consequence, the standard approach which con- structs change-point detection procedures based on asymptotically optimal open- ended tests does not in general provide asymptotically optimal procedures for de- pendent observations.

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