# Robust Variable Selection and Estimation Via Adaptive Elastic Net S-Estimators for Linear Regression

arXiv: https://arxiv.org/abs/2107.03325 · HTML: https://mlsanity.com/paper/2107.03325/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 7 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [Adaptive Huber Regression](https://mlsanity.com/paper/1706.06991/) (2017)
- [Statistical consistency and asymptotic normality for high-dimensional robust M-estimators](https://mlsanity.com/paper/1501.00312/) (2015)
- [A Study of Error Variance Estimation in Lasso Regression](https://mlsanity.com/paper/1311.5274/) (2013)
- [Scale calibration for high-dimensional robust regression](https://mlsanity.com/paper/1811.02096/) (2018)
- [Simultaneous Feature Selection and Outlier Detection with Optimality Guarantees](https://mlsanity.com/paper/2007.06114/) (2020)
- [Iteratively Reweighted ℓ1-Penalized Robust Regression](https://mlsanity.com/paper/1907.04027/) (2019)

## Built on by (most cited first, 1 of 1)

- [The Adaptive τ-Lasso: Robustness and Oracle Properties](https://mlsanity.com/paper/2304.09310/) (2023)

## Abstract (arXiv)

Heavy-tailed error distributions and predictors with anomalous values are ubiquitous in high-dimensional regression problems and can seriously jeopardize the validity of statistical analyses if not properly addressed. For more reliable estimation under these adverse conditions, we propose a new robust regularized estimator for simultaneous variable selection and coefficient estimation. This estimator, called adaptive PENSE, possesses the oracle property without prior knowledge of the scale of the residuals and without any moment conditions on the error distribution. The proposed estimator gives reliable results even under very heavy-tailed error distributions and aberrant contamination in the predictors or residuals. Importantly, even in these challenging settings variable selection by adaptive PENSE remains stable. Numerical studies on simulated and real data sets highlight superior finite-sample performance in a vast range of settings compared to other robust regularized estimators in the case of contaminated samples and competitiveness compared to classical regularized estimators in clean samples.