The Propagation-Separation Approach: Consequences of model misspecification

The article presents new results on the Propagation-Separation Approach by Polzehl and Spokoiny [2006]. This iterative procedure provides a unified approach for nonparametric estimation, sup- posing a local parametric model. The adaptivity of the estimator ensures sensitivity to structural changes. Originally, an additional memory step was included into the algorithm, where most of the theoretical prop- erties were based on. However, in practice, a simplified version of the algorithm is used, where the mem- ory step is omitted. Hence, we aim to justify this simplified procedure by means of a theoretical study and numerical simulations. In our previous study [Becker and Math\'e, 2013], we analyzed the simplified Propagation-Separation Approach, supposing piecewise constant parameter functions with sharp discon- tinuities. Here, we consider the case of a misspecified model.