Complexity L0-Penalized M-Estimation: Consistency in More Dimensions
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Author / Producer
Date
2013-09
Publication Type
Journal Article
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yes
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Abstract
We study the asymptotics in L2 for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains—e.g., images—by piecewise smooth functions. We introduce a fairly general setting, which comprises most of the presently popular partitions of signal or image domains, like interval, wedgelet or related partitions, as well as Delaunay triangulations. Then, we prove consistency and derive convergence rates. Finally, we illustrate by way of relevant examples that the abstract results are useful for many applications.
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published
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Journal / series
Volume
2 (3)
Pages / Article No.
311 - 344
Publisher
MDPI
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Edition / version
Methods
Software
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Date collected
Date created
Subject
Adaptive estimation; Penalized M-estimation; Potts functional; Complexity penalized; Variational approach; Consistency; Convergence rates; Wedgelet partitions; Delaunay triangulations
Organisational unit
03232 - Gutknecht, Jürg (emeritus)