JSM 2005 Online Program

Abstract #304848

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Activity Number:	468
Type:	Invited
Date/Time:	Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor:	Section on Statistical Computing
Abstract - #304848
Title:	Estimation of Discontinuous Curves and Surfaces: Edge-preserving and Smoothing
Author(s):	Irene Gijbels*+
Companies:	Catholic University of Louvain
Address:	Institute of Statistics, Louvain-La-Neuve, , Belgium
Keywords:	images ; jump-preserving ; nonparametric curve estimation ; regression surfaces ; smoothing
Abstract:	When estimating a regression curve or surface that is possibly discontinuous in certain regions, one would like to have an estimate that preserves the jumps but shows a smooth behavior at continuous regions. This talk will discuss a nonparametric estimation method that searches for compromising between the properties of jump-preserving and smoothing. In curve estimation, the method vchooses, in each point, among three estimates: a local linear estimate using only data to the left of the point, a local linear estimate based on only data to the right, and a local linear estimate using data in a two-sided neighborhood around the point. The data driven choice among the three estimates is made by comparing, in some appropriate way, the weighted residual mean squares of the three fits. This results in a consistent estimate. The proposed procedure also can be used for image denoising or estimating regression surfaces in the case of fixed or random design. Simulations will illustrate the performance of the estimation method. Applications to curve/surface estimation and image denoising will be shown.

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