Geodesic
Smoothing and preservation of irregularities using local linear fitting
Applications of Mathematics, Tome 53 (2008) no. 3, pp. 177-194.

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For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.
DOI : 10.1007/s10492-008-0003-3
Classification : 62G05, 62G07, 62G08, 62G20
Keywords: density estimation; irregularities; jumps; local linear fitting; mean; peaks; preservation; smoothing; variance 
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     title = {Smoothing and preservation of irregularities using local linear fitting},
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Gijbels, Irène. Smoothing and preservation of irregularities using local linear fitting. Applications of Mathematics, Tome 53 (2008) no. 3, pp. 177-194. doi : 10.1007/s10492-008-0003-3. http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0003-3/

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