Regression clustering with redescending M-estimators

We use the local maxima of a redescending M-estimator to identify clusters, a method proposed already by Morgenthaler (1990) for finding regression clusters. We work out the method not only for classical regression but also for orthogonal regression and multivariate locations and give consistency results for all three cases. The approach of orthogonal regression is applied to the identification of edges in noisy images.