Complexity $L^0$-penalized M-Estimation: Consistency in More Dimensions
Statistics Theory
2013-01-30 v2 Statistics Theory
Abstract
We study the asymptotics in 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.
Cite
@article{arxiv.1301.5492,
title = {Complexity $L^0$-penalized M-Estimation: Consistency in More Dimensions},
author = {Laurent Demaret and Felix Friedrich and Volkmar Liebscher and Gerhard Winkler},
journal= {arXiv preprint arXiv:1301.5492},
year = {2013}
}