Summary
Normalizing transformations of the largest and the smallest latent roots of a sample covariance matrix in a normal sample are obtained, when the corresponding population roots are simple. Using our results, confidence intervals for population roots may easily be constructed. Some numerical comparisons of the resulting approximations are made in a bivariate case, based on exact values of the probability integral of latent roots.
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Konishi, S., Sugiyama, T. Improved approximations to distributions of the largest and the smallest latent roots of a wishart matrix. Ann Inst Stat Math 33, 27–33 (1981). https://doi.org/10.1007/BF02480916
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DOI: https://doi.org/10.1007/BF02480916