# Robust Linear Regression: A Review and Comparison

arXiv: https://arxiv.org/abs/1404.6274 · HTML: https://mlsanity.com/paper/1404.6274/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2014.

## Built on by (most cited first, 5 of 5)

- [Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks](https://mlsanity.com/paper/2210.10646/) (2022)
- [Efficient Sparse Least Absolute Deviation Regression with Differential Privacy](https://mlsanity.com/paper/2401.01294/) (2024)
- [RIGID: Robust Linear Regression with Missing Data](https://mlsanity.com/paper/2205.13635/) (2022)
- [On the Oracle Complexity of Higher-Order Smooth Non-Convex Finite-Sum Optimization](https://mlsanity.com/paper/2103.05138/) (2021)
- [On robust recovery of signals from indirect observations](https://mlsanity.com/paper/2501.01935/) (2025)

## Abstract (arXiv)

Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article aims to review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios.