Partial differential equations for hypergeometric functions of complex argument matrices and their applications

  • Yasuko Chikuse
Article

Keywords

Asymptotic Expansion Latent Root Hypergeometric Function Confluent Hypergeometric Function Standard Normal Distribution Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Brillinger, D. R. (1969). The canonical analysis of stationary time series, inMultivariate Analysis-II (P. R. Krishnaiah, Ed.), pp. 331–350. Academic Press, New York.Google Scholar
  2. [2]
    Chikuse, Y. (1974) Asymptotic expansions for the distributions of the latent roots of two matrices in multivariate analysis, Ph.D. thesis. Yale University.Google Scholar
  3. [3]
    Constantine, A. G. and Muirhead, R. J. (1972). Partial differential equations for hypergeometric functions of two argument matrices.J. Multivariate Analysis,2, 332–338.CrossRefMathSciNetMATHGoogle Scholar
  4. [4]
    Fujikoshi, Y. (1971) Asymptotic expansions of the non-null distributions of two criteria for the linear hypothesis concerning complex multivariate normal populations,Ann. Inst. Statist. Math.,23, 477–490.CrossRefMathSciNetMATHGoogle Scholar
  5. [5]
    Goodman, N. R. (1963). Statistical analysis based on a certain multivariate complex Gaussian distribution,Ann. Math. Statist.,35, 152–176.Google Scholar
  6. [6]
    Goodman, N. R. and Dubman, M. R. (1969). Theory of time-varying spectral analysis and complex Wishart matrix processes, inMultivariate Analysis-II (P. R. Krishnaiah, Ed.), pp. 351–366, Academic Press, New York.Google Scholar
  7. [7]
    Hayakawa, T. (1972). On the distribution of the latent roots of a complex Wishart matrix (non-central case),Ann. Inst. Statist. Math.,24, 1–17.CrossRefMathSciNetMATHGoogle Scholar
  8. [8]
    Hayakawa, T. (1972). The asymptotic distributions of the statistics based on the complex Gaussian distribution,Ann. Inst. Statist. Math.,24, 231–244.CrossRefMathSciNetMATHGoogle Scholar
  9. [9]
    Herz, C. S. (1955). Bessel functions of matrix argument,Ann. Math.,61, 474–523.CrossRefMathSciNetGoogle Scholar
  10. [10]
    James, A. T. (1964). Distribution of matrix variates and latent roots derived from normal samples,Ann. Math. Statist.,35, 475–501.MathSciNetMATHGoogle Scholar
  11. [11]
    James, A. T. (1968). Calculation of zonal polynomial coefficients by use of the Laplace-Beltrami operator,Ann. Math. Statist.,39, 1711–1718.MathSciNetMATHGoogle Scholar
  12. [12]
    Kendall, M. G. and Stuart, A. (1969).The Advanced Theory of Statistics, Vol. 1, Hafner, New York.MATHGoogle Scholar
  13. [13]
    Khatri, C. G. (1964). Distribution of the largest or the smallest characteristics root under null hypothesis concerning complex multivariate normal populations,Ann. Math. Statist.,35, 1807–1810.MathSciNetMATHGoogle Scholar
  14. [14]
    Khatri, C. G. (1965), Classical statistical analysis based on a certain multivariate complex Gaussian distribution,Ann. Math. Statist.,36, 98–114.MathSciNetMATHGoogle Scholar
  15. [15]
    Khatri, C. G. (1966). On the distribution problems based on positive definite quadratic functions in normal vectors,Ann. Math. Statist.,37, 468–479.MathSciNetMATHGoogle Scholar
  16. [16]
    Khatri, C. G. (1969). Non-central distributions of ith largest characteristic roots of three matrices concerning complex multivariate normal populations,Ann. Inst. Statist. Math.,21, 23–32.MathSciNetMATHGoogle Scholar
  17. [17]
    Li, H. C., Pillai, K. S. C. and Chang, T. C. (1970). Asymptotic expansions for distributions of the roots of two matrices from classical and complex Gaussian populations.Ann. Math. Statist.,41, 1541–1556.MathSciNetMATHGoogle Scholar
  18. [18]
    Muirhead, R. J. (1970). Systems of partial differential equations for hypergeometric functions of matrix argument,Ann. Math. Statist.,41, 991–1001.MathSciNetMATHGoogle Scholar
  19. [19]
    Muirhead, R. J. (1970). Asymptotic distributions of some multivariate tests,Ann. Math. Statist.,41, 1002–1010.MathSciNetMATHGoogle Scholar
  20. [20]
    Muirhead, R. J. (1972). The asymptotic non-central distribution of Hotelling's generalizedT 02 Ann. Math. Statist.,43, 1671–1677.MathSciNetMATHGoogle Scholar
  21. [21]
    Muirhead, R. J. and Chikuse, Y. (1975). Asymptotic expansions for the joint and marginal distributions of the latent roots of the covariance matrix,Ann. Statist.,3, 1011–1017.MathSciNetMATHGoogle Scholar
  22. [22]
    Priestley, M. B., Subba Rao, T. and Tong, H. (1973). Identification of the structure of multivariable stochastic systems, inMultivariate Analysis-III (P. R. Krishnaiah, Ed.), pp. 351–368. Academic Press, New York.Google Scholar
  23. [23]
    Sugiura, N. (1973). Derivatives of the characteristic root of a symmetric or a Hermitian matrix with two applications in multivariate analysis,Commun. Statist.,1, 393–417.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Sugiyama, T. (1972). Distributions of the largest latent root of the multivariate complex Gaussian distribution,Ann. Inst. Statist. Math.,24, 87–94.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics 1976

Authors and Affiliations

  • Yasuko Chikuse
    • 1
  1. 1.Radiation Effects Research FoundationHiroshima

Personalised recommendations