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Simultaneous tests for equality of latent roots against certain alternatives—I

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References

  1. Pillai, K. C. S., Al-Ani, S. and Jouris, G. M. (1969). On the distribution of the ratios of the roots of a covariance matrix and Wilk's criterion for tests of three hypothesesAnn. Math. Statist.,40, 2033–2040.

    MathSciNet  Google Scholar 

  2. Anderson, G. A. (1965) An asymptotic expansion for the distribution of the latent roots of the estimated covariance matrix,Ann. Math. Statist.,36, 1153–1173.

    MathSciNet  Google Scholar 

  3. Anderson, T. W. (1963). Asymptotic theory for principle component analysis,Ann. Math. Statist.,34, 122–148.

    MathSciNet  Google Scholar 

  4. Constantine, A. G. (1963). Some noncentral distribution problems in multivariate analysis,Ann. Math. Statist.,34, 1270–1285.

    MathSciNet  Google Scholar 

  5. Grishick, M. A. (1941). The distribution of the ellipticity statistic Le when the hypothesis is false,Terrstrial Magnetism and Atmospheric Electricity,46, 455–457.

    Google Scholar 

  6. James, A. T. (1960). The distribution of the latent roots of the covariance matrix.Ann. Math. Statist.,31, 151–158.

    MathSciNet  Google Scholar 

  7. James, A. T. (1961). The distribution of noncentral means with known covariance.Ann. Math. Statist.,32, 874–882.

    MathSciNet  Google Scholar 

  8. James, A. T. (1964). Distributions of matrix variates and latent roots derived from normal sample,Ann. Math. Statist.,35, 475–501.

    MathSciNet  Google Scholar 

  9. James, A. T. (1966) Inference on latent roots by calculation of hypergeometric functions of matrix arguments. InMultivariate Analysis (P. R. Krishnaiah, ed.) Academic Press, New York, 209–235.

    Google Scholar 

  10. James, A. T. (1969). Tests of equality of latent roots of the covariance matrix. InMultivariate Analysis-II (P. R. Krishnaiah, ed.) Academic Press, New York, 205–217.

    Google Scholar 

  11. Khatri, C. G. (1967). Some distribution problems connected with the characteristic roots ofS 1 S 2 −1,Ann. Math. Statist.,38, 944–948.

    MathSciNet  Google Scholar 

  12. Krishnaiah, P. R. and Waikar, V. B. (1969) Simultaneous tests for equality of latent roots against certain alternatives-II, ARL 69-0178, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.

    Google Scholar 

  13. Mehta, M. L. (1967).Random Matrices, Academic Press, New York.

    MATH  Google Scholar 

  14. Roy, S. N. (1957).Some Aspects of Multivariate Analysis, John Wiley and Sons, Inc., New York.

    Google Scholar 

  15. Srivastava, J. N. (1966). Some generalizations of multivariate analysis of variance. InMultivariate Analysis (P. R. Krishnaiah, ed.) Academic Press, New York, 129–144.

    Google Scholar 

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The work of this author was performed at the Aerospace Research Laboratories while in the capacity of an Ohio State University Research Foundation Visiting Research Associate under Contract F 33 615 C 1758.

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Krishnaiah, P.R., Waikar, V.B. Simultaneous tests for equality of latent roots against certain alternatives—I. Ann Inst Stat Math 23, 451–468 (1971). https://doi.org/10.1007/BF02479243

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