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Biometrika 1984 71(3):561-567; doi:10.1093/biomet/71.3.561
© 1984 by Biometrika Trust
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Optimal bounds for the distributions of some test criteria for tests of dimensionality

JAMES R. SCHOTT

Department of Statistics, University of Central Florida Orlando, Florida, U.S.A.

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 {Delta} of rank r. These bounds are then used to investigate the chi-squared approximation for some test criteria used in tests of dimensionality.

Key Words: Chi-squared approximation • Discriminant function • Distribution of latent roots • Multivariate analysis of variance • Small sample size


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