Slope heuristics for multiple change-point models

With regard to multiple change-point models, much effort has been devoted to the selection of the number of change points. But, the proposed approaches are either dedicated to specific segment models or give unsatisfactory results for short or medium length sequences. We propose to apply the slope heuristic, a recently proposed non-asymptotic penalized likelihood criterion, for selecting the number of change points. In particular we apply the data-driven slope estimation method, the key point being to define a relevant penalty shape. The proposed approach is illustrated using two benchmark data sets.