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The Propagation-Separation approach is an iterative procedure for pointwiseestimation of local constant and local polynomial functions. The estimator isdefined as a weighted mean of the observations with data-driven weights. Withinhomogeneous regions it ensures a similar behavior as non-adaptive smoothing(propagation), while avoiding smoothing among distinct regions (separation). Inorder to enable a proof of stability of estimates, the authors of the originalstudy introduced an additional memory step aggregating the estimators of thesuccessive iteration steps. Here, we study theoretical properties of thesimplified algorithm, where the memory step is omitted. In particular, weintroduce a new strategy for the choice of the adaptation parameter yieldingpropagation and stability for local constant functions with sharpdiscontinuities.

A new perspective on the Propagation-Separation approach: Taking advantage of the propagation condition