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December 2009 Approximate null distribution of the largest root in multivariate analysis
Iain M. Johnstone
Ann. Appl. Stat. 3(4): 1616-1633 (December 2009). DOI: 10.1214/08-AOAS220


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.


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Iain M. Johnstone. "Approximate null distribution of the largest root in multivariate analysis." Ann. Appl. Stat. 3 (4) 1616 - 1633, December 2009.


Published: December 2009
First available in Project Euclid: 1 March 2010

zbMATH: 1184.62083
MathSciNet: MR2752150
Digital Object Identifier: 10.1214/08-AOAS220

Keywords: Canonical correlation , characteristic root , equality of covariance matrices , greatest root statistic , Largest eigenvalue , MANOVA , multivariate linear model , Tracy–Widom distribution

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 4 • December 2009
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