Regression Residuals, Moments, and Their Use in Tests for Normality

Abstract

In linear regression the unknown true errors are often estimated by the ordinary least squares residuals. These estimates suffer from shrinkage and superimposed normality effects and may give a misleading impression of the true error distribution. A new method, RMOLS, is proposed to improve the estimation of moments by suitably rescaling the moment estimators obtained from least squares residuals. These RMOLS moments give better estimates of skewness and kurtosis coefficients and better power for one class of tests for normality. These properties are demonstrated by a Monte Carlo study under a variety of random error distributions.

Keywords:

• Regression residuals
• Rescaled moments
• Tests for normality
• Power simulation

Acknowledgment

The author gratefully acknowledges valuable comments and suggestions of the referee. He also wishes to thank him for pointing out some computational mistakes that occurred in the power simulation experiment.