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A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions

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  • Kakizawa, Yoshihide
  • Iwashita, Toshiya

Abstract

The purpose of this paper is to investigate the effect of nonnormality upon the nonnull distributions of some MANOVA test statistics under normality. It is shown that whatever the underlying distributions, the difference of the local powers up to order N-1 (N is the total number of observations) after either Bartlett's type adjustment or Cornish-Fisher's type adjustment under nonnormality coincides with that in Anderson [An Introduction to Multivariate Statistical Analysis, second ed., 1984 and third ed., 2003, Wiley, New York] under normality. The performance of higher-order results in finite samples is examined using simulation studies.

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  • Kakizawa, Yoshihide & Iwashita, Toshiya, 2008. "A comparison of higher-order local powers of a class of one-way MANOVA tests under general distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1128-1153, July.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:6:p:1128-1153
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    1. Cribari-Neto, Francisco & Ferrari, Silvia L. P., 2001. "Monotonic improved critical values for two [chi]2 asymptotic criteria," Economics Letters, Elsevier, vol. 71(3), pages 307-316, June.
    2. Fujikoshi, Yasunori, 1997. "An Asymptotic Expansion for the Distribution of Hotelling'sT2-Statistic under Nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 187-193, May.
    3. Fujikoshi, Yasunori, 1988. "Comparison of powers of a class of tests for multivariate linear hypothesis and independence," Journal of Multivariate Analysis, Elsevier, vol. 26(1), pages 48-58, July.
    4. Mukerjee, R. & Gupta, A. S., 1993. "Comparison between the Locally Most Mean Power Unbiased and Rao's Tests in the Multiparameter Case," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 9-24, April.
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    Cited by:

    1. Bodnar, Olha & Touli, Elena Farahbakhsh, 2023. "Exact test theory in Gaussian graphical models," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
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    3. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2019. "Testing for independence of large dimensional vectors," MPRA Paper 97997, University Library of Munich, Germany, revised May 2019.
    4. Kakizawa, Yoshihide, 2012. "Improved chi-squared tests for a composite hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 141-161.

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