Multiple Linear Regression Model Under Nonnormality

Abstract

We consider multiple linear regression models under nonnormality. We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust. We show that the least squares esimators are considerably less efficient. We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient. We provide real-life examples.

Key Words:

• Multiple linear regression
• Modified likelihood
• Robustness
• Outliers
• M estimators
• Least squares
• Nonnormality
• Hypothesis testing

Acknowledgment

We are grateful to the referee for very helpful comments.