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An asymptotic expansion of the distribution of Student's t type statistic under spherical distributions

Author

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  • Iwashita, Toshiya
  • Kakizawa, Yoshihide
  • Inoue, Tatsuki
  • Seo, Takashi

Abstract

An asymptotic expansion of the distribution of Student's t type statistic based on the multivariate standardized or studentized sample mean vector is obtained by making use of an Edgeworth expansion up to the order O(N-2), where N is sample size and Student's t type transformation is defined by for any , . It turns out that a t-approximation to Student's t type statistic based on the studentized sample mean vector has the error o(N-l), if a certain spherical population has at least 4(l+1)th moment, where l=0,1,2. Some numerical experiments are also conducted to evaluate the accuracy of the result.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:18:p:1935-1942
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    References listed on IDEAS

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    1. Jensen, D. R., 1994. "Closure of multivariate t and related distributions," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 307-312, July.
    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. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, November.
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    Cited by:

    1. Iwashita, Toshiya & Klar, Bernhard, 2014. "The joint distribution of Studentized residuals under elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 203-209.

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