Rank Scores Suitable for Analyses of Linear Models Under Asymmetric Error Distributions

Abstract

Linear models having asymmetric error distributions often occur in practice. In this article, rank scores suitable for skewed error distributions are proposed. Using these scores, a rank analysis of a linear model based on R estimates will tend to be a more powerful analysis than that based on scores suitable for symmetrically distributed errors or least squares. Score functions are presented for the generalized F family of error distributions. These scores are bounded, and hence the corresponding rank analysis is robust. This family contains distributions used to model lifetime data. Practical procedures for score selection are discussed, including a method to estimate the scores. Two examples are discussed in detail, along with the results of a small Monte Carlo study.

KEY WORDS:

• Asymmetric distribution
• Generalized F family of distributions
• Least squares
• q-q plots
• R estimates
• Robust procedure
• Wilcoxon scores