A Note on Asymmetry and Robustness in Linear Regression

Abstract

We discuss the assumption of symmetry in robust linear regression. It is important to distinguish between the intercept term and the slope parameters. Ordinary robust regression requires no assumption of symmetry when interest lies in slope parameters; computer programs, confidence intervals, standard errors, and so forth do not change because the errors are asymmetric. The situation is radically different for bounded-influence estimators. With the exception of the Mallows class, these estimators are inconsistent for slope when the errors are asymmetric.

Key Words:

• Asymptotic theory
• Bounded-influence estimation
• Estimating equations
• L estimation
• M estimation
• Robust regression