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Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory

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References

  1. Bingham, C. (1974). An identity involving partitional generalized binomial coefficients,J. Multivariate Anal.,4, 210–223.

    Article  MathSciNet  Google Scholar 

  2. Constantine, A. G. (1963). Some non-central distribution problems in multivariate analysis,Ann. Math. Statist.,34, 1270–1285.

    Article  MathSciNet  Google Scholar 

  3. Constantine, A. G. (1966). The distribution of Hotelling's generalizedT 0 2,Ann. Math. Statist.,37, 215–225.

    Article  MathSciNet  Google Scholar 

  4. Crowther, N. A. S. (1975). The exact non-central distribution of a quadratic form in normal vectors,S. Afr. Statist. J.,9, 27–36.

    MathSciNet  MATH  Google Scholar 

  5. Davis, A. W. (1976). Statistical distributions in univariate and multivariate Edgeworth populations,Biometrika,63, 661–670.

    Article  MathSciNet  Google Scholar 

  6. Davis, A. W. (1980). Invariant polynomials with two matrix arguments, extending the zonal polynomials,Multivariate Analysis—V (ed. P. R. Krishnaiah), 287–299.

  7. Hayakawa, T. (1967). On the distribution of the maximum latent root of a positive definite symmetric random matrix,Ann. Inst. Statist. Math.,19, 1–17.

    Article  MathSciNet  Google Scholar 

  8. Hayakawa, T. (1969). On the distribution of the latent roots of a positive definite random symmetric matrix I,Ann. Inst. Statist. Math.,21, 1–21.

    Article  MathSciNet  Google Scholar 

  9. Hayakawa, T. (1972). On the distribution of the multivariate quadratic form in multivariate normal samples,Ann. Inst. Statist. Math.,24, 205–230.

    Article  MathSciNet  Google Scholar 

  10. Hayakawa, T. (1973). An asymptotic expansion for the distribution of the determinant of a multivariate quadratic form in a normal sample,Ann. Inst. Statist. Math.,25, 395–406.

    Article  MathSciNet  Google Scholar 

  11. Herz, C. S. (1955). Bessel functions of matrix argument,Ann. Math.,61, 474–523.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. Khatri, C. G. (1977). Distribution of a quadratic form in noncentral normal vectors using generalised Laguerre polynomials,S. Afr. Statist. J.,11, 167–179.

    MathSciNet  MATH  Google Scholar 

  14. Pillai, K. C. S. (1975). The distribution of the characteristic roots ofS 1 S 2 −1 under violations,Ann. Statist.,3, 773–779.

    Article  MathSciNet  Google Scholar 

  15. Pillai, K. C. S. and Sudjana (1975). Exact robustness studies of tests of two multivariate hypotheses based on four criteria and their distribution problems under violations,Ann. Statist.,3, 617–636.

    Article  MathSciNet  Google Scholar 

  16. Robinson, G. de B. (1961).Representation Theory of the Symmetric Group, Edinburgh University Press, Edinburgh.

    MATH  Google Scholar 

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  1. A. W. Davis
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Davis, A.W. Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory. Ann Inst Stat Math 31, 465–485 (1979). https://doi.org/10.1007/BF02480302

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  • DOI: https://doi.org/10.1007/BF02480302

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