Structural Adaptive Smoothing by Propagation–Separation Methods

Abstract

Regression is commonly used to describe and analyze the relation between explanatory input variables X and one or multiple responses Y. In many applications such relations are too complicated to model with a parametric regression function. Classical nonparametric regression (see e.g., Fan and Gijbels, 1996;Wand and Jones, 1995; Loader, 1999; Simonoff, 1996) and varying coefficient models (see e.g., Hastie and Tibshirani, 1993; Fan and Zhang, 1999; Carroll et al., 1998; Cai et al., 2000), allow for a more flexible form. In this article we describe an approach that allows us to efficiently handle discontinuities and spatial inhomogeneities of the regression function in such models.