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Powers of the largest latent root test of $$\Sigma = I$$. (English) Zbl 0284.62026
Summary: In this paper two types of asymptotic approximations to the distribution of the largest latent root of the sample covariance matrix are examined. The first approximation is valid when the largest latent root of the population covariance matrix $$\Sigma$$ is simple, in which case the limiting distribution is normal, and the second approximation is valid when $$\Sigma = \lambda I$$. These approximations are used to compute powers of the test of the hypothesis $$\Sigma= I$$ in the bivariate and trivariate cases.

##### MSC:
 62H15 Hypothesis testing in multivariate analysis 62E20 Asymptotic distribution theory in statistics 62H10 Multivariate distribution of statistics
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