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An asymptotic expansion of the distribution of Rao's U-statistic under a general condition

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  • Gupta, Arjun K.
  • Xu, Jin
  • Fujikoshi, Yasunori

Abstract

In this paper we consider the problem of testing the hypothesis about the sub-mean vector. For this propose, the asymptotic expansion of the null distribution of Rao's U-statistic under a general condition is obtained up to order of n-1. The same problem in the k-sample case is also investigated. We find that the asymptotic distribution of generalized U-statistic in the k-sample case is identical to that of the generalized Hotelling's T2 distribution up to n-1. A simulation experiment is carried out and its results are presented. It shows that the asymptotic distributions have significant improvement when comparing with the limiting distributions both in the small sample case and the large sample case. It also demonstrates the equivalence of two testing statistics mentioned above.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:492-513
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    References listed on IDEAS

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    1. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    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.
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    Cited by:

    1. Tamae Kawasaki & Toshiki Naito & Takashi Seo, 2020. "T^2 Type Test Statistic and Simultaneous Confidence Intervals for Two Sub-mean Vectors," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-1, January.
    2. Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.

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