Robust linear regression: A review and comparison

ABSTRACT

Ordinary least-square (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.

KEYWORDS:

• Breakdown point
• Linear regression
• Outliers
• Robustness

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F35
• 62J05

Funding

Weixin Yao’s research is supported by NSF grant DMS-1461677 and Department of Energy with the award No: 10006272.