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An Asymptotic Expansion for the Distribution of Hotelling'sT2-Statistic under Nonnormality

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  • Fujikoshi, Yasunori

Abstract

In this paper we obtain an asymptotic expansion for the distribution of Hotelling'sT2-statisticT2under nonnormality when the sample size is large. In the derivation we find an explicit Edgeworth expansion of the multivariatet-statistic. Our method is to use the Edgeworth expansion and to expand the characteristic function ofT2.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:61:y:1997:i:2:p:187-193
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    References listed on IDEAS

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    1. Bhattacharya, Rabi N. & Ghosh, J. K., 1988. "On moment conditions for valid formal Edgeworth expansions," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 68-79, October.
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    Cited by:

    1. Iwashita, Toshiya & Kakizawa, Yoshihide & Inoue, Tatsuki & Seo, Takashi, 2009. "An asymptotic expansion of the distribution of Student's t type statistic under spherical distributions," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1935-1942, September.
    2. Kakizawa, Yoshihide, 2016. "Some integrals involving multivariate Hermite polynomials: Application to evaluating higher-order local powers," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 162-168.
    3. Gupta, Arjun K. & Xu, Jin & Fujikoshi, Yasunori, 2006. "An asymptotic expansion of the distribution of Rao's U-statistic under a general condition," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 492-513, February.
    4. Loperfido, Nicola, 2014. "Linear transformations to symmetry," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 186-192.
    5. Yujun Wu & Marc G. Genton & Leonard A. Stefanski, 2006. "A Multivariate Two-Sample Mean Test for Small Sample Size and Missing Data," Biometrics, The International Biometric Society, vol. 62(3), pages 877-885, September.
    6. Akita, Tomoyuki & Jin, Jinghua & Wakaki, Hirofumi, 2010. "High-dimensional Edgeworth expansion of a test statistic on independence and its error bound," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1806-1813, September.
    7. Kakizawa, Yoshihide, 2008. "Multiple comparisons of several heteroscedastic multivariate populations," Statistics & Probability Letters, Elsevier, vol. 78(11), pages 1328-1338, August.
    8. 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.

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