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Thu, 11 Oct 2007 12:37:44 +0200Thu, 11 Oct 2007 12:37:44 +0200Some asymptotics for local least-squares regression with regularization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1902
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.Jürgen Franke; Joseph Tadjuidje; Stefan Didas; Joachim Weickertpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1902Thu, 11 Oct 2007 12:37:44 +0200