Robust Linear Regression: A Review and Comparison

TL;DR

This paper reviews and compares various robust linear regression methods, focusing on their breakdown points and efficiency, supported by simulation studies and real data applications.

Contribution

It provides a comprehensive review and comparison of robust linear regression techniques, including recent developments, highlighting their strengths and limitations.

Findings

Robust methods vary in breakdown point and efficiency.

Simulation studies show performance differences under various scenarios.

Real data application demonstrates practical effectiveness.

Abstract

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.