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Varying coefficient regression modeling by adaptive weights smoothing

Please always quote using this URN:urn:nbn:de:0296-matheon-702
  • The adaptive weights smoothing (AWS) procedure was introduced in Polzehl and Spokoiny (2000) in the context of image denoising. The procedure has some remarkable properties like preservation of edges and contrast, and (in some sense) optimal reduction of noise. The procedure is fully adaptive and dimension free. Simulations with artificial images show that AWS is superior to classical smoothing techniques especially when the underlying image function is discontinuous and can be well approximated by a piecewise constant function. However, the latter as- sumption can be rather restrictive for a number of potential applications. Here the AWS method is generalized to the case of an arbitrary local lin- ear parametric structure. We also establish some important results about properties of the AWS procedure including the so called "propagation condition" and spatial adaptivity. The performance of the procedure is illustrated by examples for local polynomial regression in univariate and bivariate situations.

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Metadaten
Author:Jörg Polzehl, Vladimir Spokoiny
URN:urn:nbn:de:0296-matheon-702
Referee:Christof Schütte
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2004/02/16
Release Date:2004/01/29
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Preprint Number:83
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