Some Contributions to Robust Nonparametric Smoothing

Abstract

This talk is divided into three parts, all concerns with M-type robust nonparametric smoothing. The first part of the talk presents a fast, widely applicable algorithm for computing the M-type regression estimates. We shall demonstrate its applicability by applying it to robust wavelet regression and robust penalized regression spline fitting. Both numerical and theoretical results will be provided. In the second part we discuss the issue of automatic selection of the cutoff value of the Huber loss function. Two approaches are currently being investigated. The first approach provides an answer to the "binary decision": should we use robust smoothing or not at all. The second approach attempts to select a "best" value for the cutoff. Lastly a robust version of SiZer (Chaudhuri & Marron 1999) will be presented. This robust SiZer can be applied to explore regression structures hidden in noisy data sets and also to identify outliers.