Curve Fitting Under Jump and Peak Irregularities Using Local Linear Regression

Abstract

In Desmet and Gijbels (2009), the problem of curve fitting on functions with peaks was addressed and a method was proposed that was building further on the one used in Gijbels et al. (2007) when dealing with functions that have jump discontinuities. In this article, we propose a common framework for both estimation problems and an integrated procedure where an appropriate diagnostic quantity is a key ingredient. In particular we discuss practical procedure parameter selection considering target functions with an unknown number of irregularities of unknown type. The method is illustrated both on simulated and real life data sets.