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A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations


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  • Solomon Harrar


  • Arne Bathke


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    Bibliographic Info

    Article provided by Springer in its journal Annals of the Institute of Statistical Mathematics.

    Volume (Year): 64 (2012)
    Issue (Month): 1 (February)
    Pages: 135-165

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    Handle: RePEc:spr:aistmt:v:64:y:2012:i:1:p:135-165

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    Keywords: MANOVA; Perturbation method; Heteroscedasticity; Non-normality; Local alternatives; Multivariate tests;


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    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Yasunori Fujikoshi, 1975. "Asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis," Annals of the Institute of Statistical Mathematics, Springer, vol. 27(1), pages 99-108, December.
    3. Boos, Dennis D. & Brownie, Cavell, 1995. "ANOVA and rank tests when the number of treatments is large," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 183-191, May.
    4. Arjun Gupta & Solomon Harrar & Yasunori Fujikoshi, 2008. "MANOVA for large hypothesis degrees of freedom under non-normality," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(1), pages 120-137, May.
    5. Harrar, Solomon W. & Bathke, Arne C., 2008. "Nonparametric methods for unbalanced multivariate data and many factor levels," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1635-1664, September.
    6. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix: Some properties and applications," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153207, Tilburg University.
    7. Kakizawa, Yoshihide, 2009. "Third-order power comparisons for a class of tests for multivariate linear hypothesis under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 473-496, March.
    8. Solomon Harrar & Arjun Gupta, 2007. "Asymptotic Expansion for the Null Distribution of the F-statistic in One-way ANOVA under Non-normality," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(3), pages 531-556, September.
    9. Gupta, Arjun K. & Harrar, Solomon W. & Fujikoshi, Yasunori, 2006. "Asymptotics for testing hypothesis in some multivariate variance components model under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 148-178, January.
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