Complexity L0-Penalized M-Estimation: Consistency in More Dimensions


Date

2013-09

Publication Type

Journal Article

ETH Bibliography

yes

Citations

Altmetric

Data

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.

Publication status

published

Editor

Book title

Journal / series

Volume

2 (3)

Pages / Article No.

311 - 344

Publisher

MDPI

Event

Edition / version

Methods

Software

Geographic location

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) check_circle

Notes

Funding

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