The Propagation-Separation Approach: Consequences of model misspecification

Abstract

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, supposing 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 properties were based on. However, in practice, a simplified version of the algorithm is used, where the memory 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 Mathé, 2013], we analyzed the simplified Propagation-Separation Approach, supposing piecewise constant parameter functions with sharp discontinuities. Here, we consider the case of a misspecified model.