The shooting S-estimator: robust regression in the independent contamination model

Classical parametric regression assumes that the observed data follow a model y_i = x_iβ + e_i with i = 1,...,n. In robust regression, however, a minority of the data may be affected by abnormal noise. Thus, the data actually comes from a mixture distribution where the dominant component follows the model above and the minority component (outliers) is unspecified. Robust techniques try to minimize the influence of those outliers. This approach, however, has some limitations. In case the contamination in the different variables is independent of each other (independent contamination model), there may not be any observations anymore that are not contaminated in any of its variables. But each observation will mainly consist of clean values for the different variables. Using the usual approach of downweighting observations as a whole, will cause most robust methods to break down. We propose an regression estimator called shooting S-estimator that takes this variablewise (cellwise) contamination into account. It combines the coordinate descent method ('shooting algorithm') with regression S-estimation. An algorithm for the computation of shooting S-estimates is provided.status: publishe