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

## TL;DR

This paper introduces robust and sparse elastic net estimators for high-dimensional linear and logistic regression, with algorithms that identify outlier-free data subsets and improve estimation accuracy, outperforming existing methods.

## Contribution

The paper develops fully robust elastic net estimators for high-dimensional regression, including algorithms for outlier detection and tuning, with demonstrated superior performance.

## Key findings

- Robust estimators outperform non-robust methods in simulations.
- Algorithms efficiently identify outlier-free data subsets.
- Proposed methods show good performance on real data.

## Abstract

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.