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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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  • Solomon Harrar & Arne Bathke, 2012. "A modified two-factor multivariate analysis of variance: asymptotics and small sample approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 135-165, February.
    • Handle: RePEc:spr:aistmt:v:64:y:2012:i:1:p:135-165
    DOI: 10.1007/s10463-010-0299-0
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    References listed on IDEAS

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    1. 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.
    2. 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;The Institute of Statistical Mathematics, vol. 59(3), pages 531-556, September.
    3. 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.
    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;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 120-137, May.
    5. 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.
    6. 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.
    7. 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;The Institute of Statistical Mathematics, vol. 27(1), pages 99-108, December.
    8. 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.
    9. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
    2. Alba-Fernández, M.V. & Jiménez-Gamero, M.D. & Jiménez-Jiménez, F., 2024. "Testing for proportions when data are classified into a large number of groups," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 588-600.
    3. Xu, Li-Wen, 2015. "Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 291-303.
    4. Jiménez-Gamero, M. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    5. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    6. Watanabe, Hiroki & Hyodo, Masashi & Nakagawa, Shigekazu, 2020. "Two-way MANOVA with unequal cell sizes and unequal cell covariance matrices in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    7. Dennis Dobler & Sarah Friedrich & Markus Pauly, 2020. "Nonparametric MANOVA in meaningful effects," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 997-1022, August.
    8. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    9. Hasler Mario, 2014. "Multiple Contrast Tests for Multiple Endpoints in the Presence of Heteroscedasticity," The International Journal of Biostatistics, De Gruyter, vol. 10(1), pages 17-28, May.
    10. Rosa Arboretti & Riccardo Ceccato & Livio Corain & Fabrizio Ronchi & Luigi Salmaso, 2018. "Multivariate small sample tests for two-way designs with applications to industrial statistics," Statistical Papers, Springer, vol. 59(4), pages 1483-1503, December.

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