Approximate null distribution of the largest root in multivariate analysis

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 setttings.

Published in at http://dx.doi.org/10.1214/08-AOAS220 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• On Orthogonal and Symplectic Matrix Ensembles
• Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy--Widom limits and rates of convergence

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