Multiscale Robust Regression, Multiscale Influence Anal- ysis and Application to Edge Detection

The Multiscale Strip Construction, or in short MSC (Lerman et al., 2007), was initially proposed to identify enriched spots in ChIP-on-chip arrays. Here we extend this method to the setting of robust high-dimensional curve estimation. We establish its robustness as well as accurateness by bounding both the empirical influence function and the empirical bias of approximation at a sufficiently large set of points. We also demonstrate in practice the robustness and accurateness of MSC by comparing it with other successful methods of robust regression on artificial data sets with significant outlier components. A new application of the high-dimensional MSC to edge detection is introduced and tested.