Asymptotic expansions of the non-null distributions of three statistics in GMANOVA

  • Yasunori Fujikoshi
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Keywords

Asymptotic Expansion Asymptotic Formula Normal Distribution Function Standard Normal Distribution Function Characteristic Func 
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References

  1. [1]
    Anderson, T. W. (1946). The noncentral Wishart distribution and certain problems of multivariate statistics,Ann. Math. Statist.,17, 409–431.MATHGoogle Scholar
  2. [2]
    Fujikoshi, Y. (1970). Asymptotic expansions of the distributions of test statistics in multivariate analysis,J. Sci. Hiroshima Univ., Ser. A-I,34, 73–144.MATHMathSciNetGoogle Scholar
  3. [3]
    Fujikoshi, Y. (1973). Asymptotic formulas for the distributions of three statistics for multivariate linear hypothesis,Ann. Inst. Statist. Math.,25, 423–437.MATHMathSciNetGoogle Scholar
  4. [4]
    Fujikoshi, Y. (1973). Monotonicity of the power functions of some tests in general MANOVA models,Ann. Statist.,1, 388–391.MATHMathSciNetGoogle Scholar
  5. [5]
    Gleser, L. J. and Olkin, I. (1970). Linear models in multivariate analysis,Essays in probability and statistics, 267–292, The University of North Carolina Monograph Series (No. 3) in Probability and Statistics.Google Scholar
  6. [6]
    Ito, K. (1956). Asymptotic formulae for the distribution of Hotelling's generalizedT 02 statistics,Ann. Math. Statist.,27, 1091–1105.MATHMathSciNetGoogle Scholar
  7. [7]
    James, G. S. (1954). Test of linear hypothesis in univariate and multivariate analysis when the ratios of the population variances are unknown,Biometrika,41, 19–43.MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Khatri, C. G. (1966). A note on a MANOVA model applied to problems in growth curve,Ann. Inst. Statist. Math.,18, 75–85.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    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.MATHMathSciNetGoogle Scholar
  10. [10]
    Olkin, I. and Shrikhande, S. S. (1954). On a modifiedT 2 problem,Ann. Math. Statist.,25, 808.Google Scholar
  11. [11]
    Potthoff, R. F. and Roy, S. N. (1964). A general multivariate analysis of variance model useful especially growth curve problems,Biometrika,51, 313–326.MATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    Rao, C. R. (1966). Covariance adjustment and related problems in multivariate analysis,Multivariate analysis, edited by P. R. Krishnaiah, 87–102, Academic Press, New York.Google Scholar
  13. [13]
    Siotani, M. (1971). An asymptotic expansion of the non-null distribution of Hotelling'sT 02-statistic,Ann. Math. Statist.,42, 560–571.MATHMathSciNetGoogle Scholar
  14. [14]
    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.MATHMathSciNetGoogle Scholar
  15. [15]
    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.MATHMathSciNetGoogle Scholar

Copyright information

© Institute of Statistical Mathematics 1974

Authors and Affiliations

  • Yasunori Fujikoshi
    • 1
  1. 1.Kobe UniversityKobeJapan

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