# Robust and sparse estimation methods for high dimensional linear and logistic regression

arXiv: https://arxiv.org/abs/1703.04951 · HTML: https://mlsanity.com/paper/1703.04951/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2017.

## Built on by (most cited first, 3 of 3)

- [Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies](https://mlsanity.com/paper/2112.08471/) (2021)
- [Robust penalized least squares of depth trimmed residuals regression for high-dimensional data](https://mlsanity.com/paper/2309.01666/) (2023)
- [Adaptive and Stratified Subsampling for High-Dimensional Robust Estimation](https://mlsanity.com/paper/2410.12367/) (2024)

## Abstract (arXiv)

Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets only. It is shown how outlier-free subsets can be identified efficiently, and how appropriate tuning parameters for the elastic net penalties can be selected. A final reweighting step improves the efficiency of the estimators. Simulation studies compare with non-robust and other competing robust estimators and reveal the superiority of the newly proposed methods. This is also supported by a reasonable computation time and by good performance in real data examples.