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Abstract:
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The largest root test is a staple of classical multivariate analysis, in canonical correlation analysis, MANOVA, multiple response linear regression and so on. It is based on the null distribution of the largest eigenvalue of A(A+B)^{-1}, where A and B are independent Wishart matrices on p variables. With appropriate centering and scaling, the Tracy-Widom law provides an approximation to the null distribution. The approximation comes from asymptotics in which the number of variables, p, is large. The purpose of this talk is to show---by numerical comparison with exact results---that the approximation may be quite adequate for applied work at conventional significance levels for small p, even as low as 2.
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