Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality
Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality
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非正态下多元线性假设检验统计量零分布的渐近展开
DOI：
10.32917/hmj/1151007641
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发表时间：
2002
影响因子：
0.2
通讯作者：
Y. Fujikoshi
中科院分区：
文献类型：
--
作者：
H. Wakaki;H. Yanagihara;Y. Fujikoshi
本文讨论了多元线性假设在非正态条件下检验统计量的分布。考虑的检验统计量包括似然比统计量、Lawley-Hotelling迹准则和Bartlett Nanda-Pillai迹准则，在正态性下。我们推导出这些检验统计量的零分布的渐近展开的顺序为n，其中n是样本大小，在非正态性。证明了我们的一般结果可以通过导出多元t-统计量分布的渐近展开式而有效地得到。作为我们的一般结果的特殊情况下，我们的渐近展开给出了Hotelling的T2统计量，单向MANOVA检验统计量等的数值精度的渐近展开近似检查。文中还讨论了扩展的有效性。此外，我们将找到条件，使Bartlett校正在正常情况下意味着一个改进的w-近似，即使在非正常。
This paper is concerned with the distributions of some test statistics for a multivariate linear hypothesis under nonnormality. The test statistics considered include the likelihood ratio statistic, the Lawley-Hotelling trace criterion and the BartlettNanda-Pillai trace criterion, under normality. We derive asymptotic expansions of the null distributions of these test statistics up to the order n , where n is the sample size, under nonnormality. It is shown that our general results can be e¤ectively obtained by deriving an asymptotic expansion of the distribution of a multivariate t-statistic. As special cases of our general results our asymptotic expansions are given for Hotelling’s T 2 statistic, one-way MANOVA test statistics, etc. Numerical accuracies of asymptotic expansion approximations are examined. The validity of the expansions is also discussed. Moreover, we will find conditions such that the Bartlett correction in the normal case implies an improved w-approximation, even under nonnormality.