Statistical Multiscale Segmentation: Inference, Algorithms and Applications

This thesis mainly concerns change-point models with independent observations from an exponential family with constant mean in between change-points. An inferential scheme for estimation and confidence statements based on a multiscale statistic is provided, which allows for efficient and accurate detection of multiple change-points. A universal bound for the asymptotic null-distribution of the considered multiscale statistic is derived. Based on this, the probability of over- and underestimation of change-points is bounded explicitly. From these bounds, model consistency is obtained and (asymptotically) honest confidence sets for the unknown change-point function and its change-points are constructed. The change-point locations are estimated at the minimax rate up to a logarithmic term. Moreover, the optimal detection rate of vanishing signals is attained. It is shown how dynamic programming can be used for efficient computation of estimators, confidence intervals and confidence bands for the change-point function. The performance and robustness of the approach are illustrated in various simulations and applications