The shooting S-estimator for robust regression

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 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.

References in corpus (3)

• Pathwise coordinate optimization
• Sparse least trimmed squares regression for analyzing high-dimensional large data sets
• Propagation of outliers in multivariate data

Cited by in corpus (8)

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• The Cellwise Minimum Covariance Determinant Estimator
• Robust Identification of Target Genes and Outliers in Triple-negative Breast Cancer Data
• Challenges of cellwise outliers
• Robust regression estimation and inference in the presence of cellwise and casewise contamination
• Outlyingness: why do outliers lie out?
• Robust Variable Selection under Cellwise Contamination
• Robust Principal Components by Casewise and Cellwise Weighting