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.

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Author:Jürgen Franke, Joseph Tadjuidje, Stefan Didas, Joachim Weickert
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