  To perform multiple regression, the least squares estimator is commonly used.
However, this estimator is not robust to outliers. Therefore, robust methods
such as S-estimation have been proposed. These estimators flag any observation
with a large residual as an outlier and downweight it in the further procedure.
However, a large residual may be caused by an outlier in only one single
predictor variable, and downweighting the complete observation results in a
loss of information.
  Therefore, we propose the shooting S-estimator, a regression estimator that
is especially designed for situations where a large number of observations
suffer from contamination in a small number of predictor variables. The
shooting S-estimator combines the ideas of the coordinate descent algorithm
with simple S-regression, which makes it robust against componentwise
contamination, at the cost of failing the regression equivariance property.
