The Role of Pseudo Data for Robust Smoothing with Application to Wavelet Regression

This paper proposes a robust curve and surface estimate based on M-type estimators and penalty based smoothing. This approach also includes an application to wavelet regression. The concept of pseudo data, a transformation of the robust additive model to one with bounded errors, is used to derive some theoretical properties and also motivate a computational algorithm. The resulting algorithm, termed the ES–algorithm, is computationally fast, simple to describe and easy to implement. It can be extended to other settings such as irregularly spaced data and image denoising. Moreover, results from a simulation study and real data examples demonstrate the promising empirical properties of the procedure.