# Robust regression based on shrinkage estimators

## TL;DR

This paper introduces a new robust linear regression estimator based on shrinkage techniques, demonstrating improved robustness and efficiency through simulations and real data applications.

## Contribution

It proposes a novel shrinkage-based robust regression estimator and thoroughly evaluates its performance against existing methods.

## Key findings

- The estimator performs well with normal and heavy-tailed errors.
- It shows robustness under data contamination.
- It is computationally efficient and affine equivariant.

## Abstract

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough simulation study is conducted to investigate: the efficiency with normal and heavy-tailed errors, the robustness under contamination, the computational times, the affine equivariance and breakdown value of the regression estimator. Two classical data-sets often used in the literature and a real socio-economic data-set about the Living Environment Deprivation of areas in Liverpool (UK), are studied. The results from the simulations and the real data examples show the advantages of the proposed robust estimator in regression.