Martingale type statistics applied to change points detection

The Shiryayev-Roberts approach has been adapted to detect various types of changes in distributions of non-i.i.d. observations. By utilizing martingale properties of Shiryayev-Roberts statistics, this technique provides distribution-free, nonasymptotic upper bounds for the significance levels of asymptotic power one tests for change points with epidemic alternatives. Since optimal Shiryayev-Roberts sequential procedures are well-investigated, the proposed methodology yields a simple approach for obtaining analytical results related to retrospective testing. In the case when distributions of data are known up to parameters, the article presents an adaptive estimation that is more efficient than a well-accepted nonanticipating estimation described in the change point literature. The proposed adaptive procedure can also be used in the context of sequential change point detection.