Generalized S-Estimators

In this article we introduce a new type of positive-breakdown regression method, called a generalized S-estimator (or GS-estimator), based on the minimization of a generalized M-estimator of residual scale. We compare the class of GS-estimators with the usual S-estimators, including least median of squares. It turns out that GS-estimators attain a much higher efficiency than S-estimators, at the cost of a slightly increased worst-case bias. We investigate the breakdown point, the maxbias curve, and the influence function of GS-estimators. We also give an algorithm for computing GS-estimators and apply it to real and simulated data.