Robust Multivariate Regression When There is Heteroscedasticity

Abstract

Rousseeuw et al. (2004) proposed a robust multivariate regression estimator and reported that its small-sample efficiency can compare favorably to ordinary least squares when the error term is homoscedastic. It is found that in terms of efficiency, their estimator performs well under heteroscedasticity, sometimes strikingly so. Several alternative estimators were considered, some of which also performed well under heteroscedasticity.

Keywords:

• Efficiency
• Outliers
• Robust methods

Mathematics Subject Classification:

• 62-07 (Data analysis)
• 62H12 (Estimation)
• 62J05 (Linear regression)