Approximate null distribution of the largest root in multivariate analysis
The Annals of Applied Statistics · 2009 · Volume 3 · Issue 4
Abstract
The greatest root distribution occurs everywhere in classical multivariate analysis, but even under the null hypothesis the exact distribution has required extensive tables or special purpose software. We describe a simple approximation, based on the Tracy–Widom distribution, that in many cases can be used instead of tables or software, at least for initial screening. The quality of approximation is studied, and its use illustrated in a variety of settings.
Keywords
Canonical correlation, characteristic root, equality of covariance matrices, greatest root statistic, Largest eigenvalue, MANOVA, multivariate linear model, Tracy–Widom distribution
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