Skip to main content
SpringerLink
Log in

Asymptotic formulas for the distributions of three statistics for multivariate linear hypothesis

  • 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

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Anderson, T. W. (1958).An Introduction to Multivariate Statistical Analysis, Wiley, New York.

    MATH  Google Scholar 

  2. Box, G. E. P. (1949). A general distribution theory for a class of likelihood criteria,Biometrika,36, 317–346.

    Article  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  4. Davis, A. W. (1970). Further applications of a differential equation for Hotelling's generalizedT 20 Ann. Inst. Statist. Math.,22, 77–86.

    MATH  MathSciNet  Google Scholar 

  5. Davis, A. W. (1970). On the null distribution of the sum of the roots of a multivariate beta distribution,Ann. Math. Statist.,41, 1557–1562.

    MATH  MathSciNet  Google Scholar 

  6. Fujikoshi, Y. (1970). Asymptotic expansions of the distributions of test statistics in multivariate analysis,J. Sci. Hiroshima Univ., Ser. A-I,34, 73–144.

    MATH  MathSciNet  Google Scholar 

  7. Hayakawa, T. (1972). On the derivation of the asymptotic distribution of the generalized Hotelling'sT 20 Ann Inst. Statist. Math.,24, 19–32.

    MATH  MathSciNet  Google Scholar 

  8. Hill, G. W. and Davis, A. W. (1968). Generalized asymptotic expansions of Cornish-Fisher type,Ann. Math. Statist.,39, 1264–1273.

    MATH  MathSciNet  Google Scholar 

  9. Hsu, P. L. (1940). On generalized analysis of variance,Biometrika,31, 221–237.

    Article  MATH  MathSciNet  Google Scholar 

  10. Ito, K. (1956). Asymptotic formulae for the distribution of Hotelling's generalizedT 20 statistic,Ann. Math. Statist.,27, 109–11105.

    Google Scholar 

  11. Ito, K. (1960). Asymptotic formulae for the distribution of Hotelling'sT 20 statistic, II,Ann. Math. Statist.,31, 1148–1153.

    MATH  MathSciNet  Google Scholar 

  12. James, Alan T. (1964). Distributions of matrix variates and latent roots derived from normal samples,Ann. Math. Statist.,39, 1711–1718.

    Google Scholar 

  13. Kitchen, J. O. (1968). Extended tables of zonal polynomials,Mimeo Series No. 565, Univ. of North Carolina.

  14. Lee, Y. S. (1971). Distribution of the canonical correlations and asymptotic expansions for the distributions of certain independence test statistics,Ann. Math. Statist.,42, 526–537.

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  16. Pillai, K. C. S. and Jayachandran, K. (1967). Power comparisons of tests of two multivariate hypotheses based on four criteria,Biometrika,54, 195–210.

    Article  MathSciNet  Google Scholar 

  17. Posten, H. O. and Bargmann, R. E. (1964). Power of the likelihood-ratio test of the general linear hypothesis in multivariate analysis,Biometrika,51, 467–480.

    Article  MATH  MathSciNet  Google Scholar 

  18. Rao, C. R. (1948). Tests of significance in multivariate analysis,Biometrika,35, 58–79.

    Article  MATH  MathSciNet  Google Scholar 

  19. Siotani, M. (1956). On the distribution of Hotelling'sT 2,Proc. Inst. Statist. Math.,4, 23–42.

    Google Scholar 

  20. Siotani, M. (1957). Note on the utilization of the generalized Student ratio in the analysis of variance or dispersion,Ann. Inst. Statist. Math.,9, 157–171.

    Article  Google Scholar 

  21. Siotani, M. (1971). An asymptotic expansion of the non-null distribution of Hotelling's generalizedT 20 -statistic,Ann. Math. Statist.,42, 560–571.

    MATH  MathSciNet  Google Scholar 

  22. Sugiura, N. and Fujikoshi, Y. (1969). Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence.Ann. Math. Statist.,40, 942–952.

    MATH  MathSciNet  Google Scholar 

  23. Sugiura, N. (1973). Further asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis,Ann. Inst. Statist. Math.,25, 153–163.

    MATH  MathSciNet  Google Scholar 

  24. Sugiura, N. and Nagao, H. (1973). Asymptotic formulas for the distributions of two trace statistics for testing independence under fixed alternative,Communications in Statistics,1, 285–295.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kobe University, Kobe, Japan

    Yasunori Fujikoshi

Authors
  1. Yasunori Fujikoshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was partially supported by the Sakko-kai Foundation.

About this article

Cite this article

Fujikoshi, Y. Asymptotic formulas for the distributions of three statistics for multivariate linear hypothesis. Ann Inst Stat Math 25, 423–437 (1973). https://doi.org/10.1007/BF02479387

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479387

Keywords

Search

Navigation