Robust regression of scattered data with adaptive spline-wavelets

A coarse-to-fine data fitting algorithm for irregularly spaced data based on boundary-adapted adaptive tensor-product semi-orthogonal spline-wavelets has been proposed in Castaño and Kunoth, 2003. This method has been extended in Castaño and Kunoth, 2005 to include regularization in terms of Sobolev and Besov norms. In this paper, we develop within this least-squares approach some statistical robust estimators to handle outliers in the data. Our wavelet scheme yields a numerically fast and reliable way to detect outliers.