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2013 A different perspective on the Propagation-Separation Approach
Saskia M. A. Becker, Peter Mathé
Electron. J. Statist. 7: 2702-2736 (2013). DOI: 10.1214/13-EJS860

Abstract

The Propagation-Separation Approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven, iteratively updated weights. Within homogeneous regions it ensures a similar behavior as non-adaptive smoothing (propagation), while avoiding smoothing among distinct regions (separation). In order to enable a proof of stability of estimates, the authors of the original study introduced an additional memory step aggregating the estimators of the successive iteration steps. Here, we study theoretical properties of the simplified algorithm, where the memory step is omitted. In particular, we introduce a new strategy for the choice of the adaptation parameter yielding propagation and stability for local constant functions with sharp discontinuities.

Citation

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Saskia M. A. Becker. Peter Mathé. "A different perspective on the Propagation-Separation Approach." Electron. J. Statist. 7 2702 - 2736, 2013. https://doi.org/10.1214/13-EJS860

Information

Published: 2013
First available in Project Euclid: 18 November 2013

zbMATH: 1283.62039
MathSciNet: MR3138835
Digital Object Identifier: 10.1214/13-EJS860

Subjects:
Primary: 62G05

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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