The Shooting S-Estimator for Robust Regression
22 Pages Posted: 22 Jan 2014
Date Written: 2013
Abstract
To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as MM-estimation have been proposed. These estimators flag any observation with a large residual as an outlier and downweight it in the further procedure. This is also the case if the large residual is caused by only one component of the observation, which 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.
Keywords: cellwise outliers, componentwise contamination, shooting algorithm, coordinate descent algorithm, regression S-estimation
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