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 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-15070
ER -