An asymptotic expansion of the distribution of Rao's U-statistic under a general condition
An asymptotic expansion of the distribution of Rao's U-statistic under a general condition
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DOI：
10.1016/j.jmva.2005.03.012
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发表时间：
2006-02
影响因子：
1.6
通讯作者：
Arjun K. Gupta;Jin Xu;Y. Fujikoshi
中科院分区：
文献类型：
--
作者：
Arjun K. Gupta;Jin Xu;Y. Fujikoshi
本文研究了次均值向量的假设检验问题。在此基础上，得到了Rao U-统计量零分布在一般条件下的n-1阶渐近展开式。同样的问题，在k样本的情况下也进行了研究。我们发现在k样本情形下，广义U统计量的渐近分布与广义Hotelling T2分布的渐近分布在n-1以内是一致的.进行了仿真实验，并给出了实验结果。结果表明，无论是在小样本情况下还是在大样本情况下，渐近分布与极限分布相比都有显著的改善。它还证明了上述两个检验统计量的等效性。
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 T2distribution 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.