On testing mean proportionality of multivariate normal variables
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This short note considers the problem of testing the null hypothesis that the mean values of two multivariate normal variables are proportional. We show that the usual likelihood ratio χ^2-test is valid non-asymptotically. Our proof relies on expressing the test statistic as the minimum eigenvalue of a Wishart variable and using a representation of its distribution using Legendre polynomials.
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