An asymptotic expansion of the distribution of Rao's U-statistic under a general condition
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.
Year of publication: |
2006
|
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Authors: | Gupta, Arjun K. ; Xu, Jin ; Fujikoshi, Yasunori |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 97.2006, 2, p. 492-513
|
Publisher: |
Elsevier |
Keywords: | Rao's U-statistic Characteristic function Multivariate Hermite polynomials Multivariate cumulants Multivariate skewness Multivariate kurtosis |
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