TY  - INPR
A1  - Franke, Jürgen
A1  - Tadjuidje, Joseph
A1  - Didas, Stefan
A1  - Weickert, Joachim
T1  - Some asymptotics for local least-squares regression with regularization
N2  - 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.
T3  - Report in Wirtschaftsmathematik (WIMA Report) - 107 
KW  - localization
KW  - regularization
KW  - smoothing
KW  - image denoising
KW  - penalization
Y1  - 2007
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1902
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-15070
ER  -