FDR-Contol in Multiscale Change-point Segmentation

Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number and size of the segments, have recently received great attention. For example, SMUCE, as introduced in (Frick, Munk, and Sieling, Multiscale change-point inference. J. R. Statist. Soc. B, 76:495-580, 2014), allows to control simultaneously over a large number of scales the error of overestimating the true number $K$ of change-points, $\mathbb{P}\{\hat K > K\} \le \alpha_S$, for a preassigned significance level $\alpha_S$, independent of the underlying change-point function. The control of this family-wise error rate (FWER), however, makes this method generally conservative. In this paper, we propose a multiscale segmentation method, which controls the false discovery rate (FDR) instead. It can be efficiently computed by a pruned dynamic program. We show a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the new segmentation method properly. By switching from FWER to FDR, the detection power of the method significantly outperforms SMUCE. The favorable performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets.