Abstract

SUMMARY

Optimal upper bounds are obtained for the distributions of two functions of the m - r smallest latent roots of HE−1, where E and H have Wishart distributions with identical covariance matrices; E has a central distribution while H has a noncentral distribution with unknown noncentrality matrix Δ of rank r. These bounds are then used to investigate the chi-squared approximation for some test criteria used in tests of dimensionality.

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