Analyzing Mean Profiles of Nonnormal Populations

Abstract

We consider testing whether the mean vectors of two or more populations have parallel, coincident, or flat profiles when the validity of normality is not known, and the sample sizes are moderate. Using some properties of multivariate moments and matrix manipulations, we obtain the asymptotic expansions for the null distribution of the Lawley–Hotelling statistics. We also derive the corresponding results in the situation where interest lies in coincidence and flatness alone. Accuracy of all the asymptotic expansions in approximating the exact null distributions is examined via simulation. Profile analysis of SO₄ concentrations from a forestry experiment is used to illustrate the methods.

Keywords:

• Asymptotic expansion
• Multivariate skewness
• Multivariate kurtosis
• MANOVA
• Repeated Measures
• Robustness

Mathematics Subject Classification:

• Primary 62H10
• Secondary 62E20