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- Title
Complexity L<sup>0</sup>-Penalized M-Estimation: Consistency in More Dimensions.
- Authors
Demaret, Laurent; Friedrich, Felix; Liebscher, Volkmar; Winkler, Gerhard
- 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.
- Subjects
ESTIMATION theory; ADAPTIVE estimation (Statistics); VARIATIONAL approach (Mathematics); CALCULUS of variations; LEAST squares
- Publication
Axioms (2075-1680), 2013, Vol 2, Issue 3, p311
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms2030311