# The shooting S-estimator for robust regression

arXiv: https://arxiv.org/abs/1506.01223 · HTML: https://mlsanity.com/paper/1506.01223/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2015.

## Built on by (most cited first, 4 of 4)

- [The Cellwise Minimum Covariance Determinant Estimator](https://mlsanity.com/paper/2207.13493/) (2022)
- [Robust penalized least squares of depth trimmed residuals regression for high-dimensional data](https://mlsanity.com/paper/2309.01666/) (2023)
- [Online and Offline Robust Multivariate Linear Regression](https://mlsanity.com/paper/2404.19496/) (2024)
- [Cellwise Outliers](https://mlsanity.com/paper/2604.14182/) (2026)

## Abstract (arXiv)

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.