Detecting multiple change-points in the mean of Gaussian process by model selection

This paper deals with the problem of detecting change-points in the mean of a signal corrupted by an additive Gaussian noise. The number of changes and their position are unknown. From a nonasymptotic point of view, we propose to estimate them with a method based on a penalized least-squares criterion. We choose the penalty function such that the resulting estimator minimizes the quadratic risk according to the results of Birgé and Massart. This penalty depends on unknown constants and we propose a calibration to obtain an automatic method. The performance of the method is assessed through simulation experiments. An application to real data is shown.