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Demaret, L. ; Friedrich, F.* ; Liebscher, V.* ; Winkler, G.*

Complexity L0-penalized M-estimation: Consistency in more dimensions.

Axioms 2, 311-344 (2013)
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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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Publication type Article: Journal article
Document type Scientific Article
Keywords Adaptive Estimation ; Complexity Penalized ; Consistency ; Convergence Rates ; Delaunay Triangulations ; Penalized M-estimation ; Potts Functional ; Variational Approach ; Wedgelet Partitions
e-ISSN 2075-1680
Journal Axioms
Quellenangaben Volume: 2, Issue: 3, Pages: 311-344 Article Number: , Supplement: ,
Publisher MDPI
Reviewing status Peer reviewed