Detecting Skewed Errors From Regression Residuals

Abstract

Symmetry of the error distribution is a common assumption in robust estimation of location and regression parameters. Tests for detecting asymmetry in the location problem are available, but their performance in regression situations is unknown. Here two such tests are investigated, and the evidence suggests two conclusions. First, the tests are valid when applied directly to either robust or least squares residuals as long as the number of parameters estimated is no more than a fourth of the sample size. Second, the effect of the design matrix on power for detecting a skewed error distribution is roughly characterized by a third-moment quantity based on least squares analysis.

KEY WORDS:

• Skewness
• Asymmetry
• Design matrix
• Linear model