Skip to main content
Log in

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

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  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. Chikuse, Y. (1974) Asymptotic expansions for the distributions of the latent roots of two matrices in multivariate analysis, Ph.D. thesis. Yale University.

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  5. Goodman, N. R. (1963). Statistical analysis based on a certain multivariate complex Gaussian distribution,Ann. Math. Statist.,35, 152–176.

    Google Scholar 

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hayakawa, T. (1972). The asymptotic distributions of the statistics based on the complex Gaussian distribution,Ann. Inst. Statist. Math.,24, 231–244.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  11. James, A. T. (1968). Calculation of zonal polynomial coefficients by use of the Laplace-Beltrami operator,Ann. Math. Statist.,39, 1711–1718.

    MathSciNet  MATH  Google Scholar 

  12. Kendall, M. G. and Stuart, A. (1969).The Advanced Theory of Statistics, Vol. 1, Hafner, New York.

    MATH  Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  14. Khatri, C. G. (1965), Classical statistical analysis based on a certain multivariate complex Gaussian distribution,Ann. Math. Statist.,36, 98–114.

    MathSciNet  MATH  Google Scholar 

  15. Khatri, C. G. (1966). On the distribution problems based on positive definite quadratic functions in normal vectors,Ann. Math. Statist.,37, 468–479.

    MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  18. Muirhead, R. J. (1970). Systems of partial differential equations for hypergeometric functions of matrix argument,Ann. Math. Statist.,41, 991–1001.

    MathSciNet  MATH  Google Scholar 

  19. Muirhead, R. J. (1970). Asymptotic distributions of some multivariate tests,Ann. Math. Statist.,41, 1002–1010.

    MathSciNet  MATH  Google Scholar 

  20. Muirhead, R. J. (1972). The asymptotic non-central distribution of Hotelling's generalizedT 20 Ann. Math. Statist.,43, 1671–1677.

    MathSciNet  MATH  Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  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. 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.

    Article  MathSciNet  Google Scholar 

  24. Sugiyama, T. (1972). Distributions of the largest latent root of the multivariate complex Gaussian distribution,Ann. Inst. Statist. Math.,24, 87–94.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Chikuse, Y. Partial differential equations for hypergeometric functions of complex argument matrices and their applications. Ann Inst Stat Math 28, 187–199 (1976). https://doi.org/10.1007/BF02504739

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02504739

Keywords

Navigation