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On the ith Latent Root of a Complex Matrix(1)

Published online by Cambridge University Press:  20 November 2018

Sabri Al-Ani
Sabri Al-Ani*
Affiliation:
University of Calgary, Calgary, Alberta
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Goodman [1] has pointed out the applications of the distributional results of the complex multivariate normal statistical analysis. Khatri [4], has suggested the maximum latent root statistic for testing the reality of a covariance matrix. The joint distribution of the latent roots under certain null hypotheses can be written as, [2], [3],

1

where

and

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 323 - 327
Copyright
Copyright © Canadian Mathematical Society 1972

Footnotes

(2)

On leave.

(1)

This research was supported by the National Science Foundation Grant GP-7663.

References

1. Goodman, N. R., Statistical analysis based on a certain multivariate complex Gaussion distribution (an introduction), Ann. Math. Stat. 34, (1963), 152-176.Google Scholar
2. Khatri, C. G., Distribution of the largest or the smallest root under null hypotheses concerning complex multivariate normal, Ann. Math. Statist. 35 (1964), 1807-1810.Google Scholar
3. Khatri, C. G., Classical statistical analysis based on a certain multivariate complex Gaussion distribution, Ann. Math. Statist. 36, (1965), 98-114.Google Scholar
4. Khatri, C. G.,A test for reality of a covariance matrix in certain complex Gaussion distribution, Ann. Math. Statist. 36, (1965), 115-119.Google Scholar
5. Pillai, K. C. S., and Dotson, C., Power comparisons of tests of two multivariate hypotheses based on individual characteristic roots, Mimeo. Series No. 108, Dept. of Statist., Purdue University, 1967.Google Scholar
6. Roy, S. N., Some aspects of multivariate analysis, Wiley, New York, 1958.Google Scholar