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

We propose a robust curve and surface estimator based on M-typeestimators and penalty-based smoothing. This approach also includesan application to wavelet regression. The concept of pseudodata, a transformation of the robust additive model to the onewith bounded errors, is used to derive some theoretical propertiesand also motivate a computational algorithm. The resulting algorithm,termed the es-algorithm, is computationally fast and providesa simple way of choosing the amount of smoothing. Moreover,it is easily described, straightforwardly implemented and canbe extended to other wavelet regression settings such as irregularlyspaced data and image denoising. Results from a simulation studyand real data examples demonstrate the promising empirical propertiesof the proposed approach.