Some asymptotics for local least-squares regression with regularization
- We derive some asymptotics for a new approach to curve estimation proposed by Mr'{a}zek et al. cite{MWB06} which combines localization and regularization. This methodology has been considered as the basis of a unified framework covering various different smoothing methods in the analogous two-dimensional problem of image denoising. As a first step for understanding this approach theoretically, we restrict our discussion here to the least-squares distance where we have explicit formulas for the function estimates and where we can derive a rather complete asymptotic theory from known results for the Priestley-Chao curve estimate. In this paper, we consider only the case where the bias dominates the mean-square error. Other situations are dealt with in subsequent papers.
Author: | Jürgen Franke, Joseph Tadjuidje, Stefan Didas, Joachim Weickert |
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URN: | urn:nbn:de:hbz:386-kluedo-15070 |
Series (Serial Number): | Report in Wirtschaftsmathematik (WIMA Report) (107) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 2007 |
Year of first Publication: | 2007 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2007/10/11 |
Tag: | image denoising; localization; penalization; regularization; smoothing |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |