Asymptotic expansion of the null distribution of one-way anova test statistic for heteroscedastic case under nonnormal1ty
Asymptotic expansion of the null distribution of one-way anova test statistic for heteroscedastic case under nonnormal1ty
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非正态下异方差情况单向方差分析检验统计量零分布的渐近展开
DOI：
10.1080/03610920008832495
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
H. Yanagihara
中科院分区：
文献类型：
--
作者：
H. Yanagihara
本文讨论了q个不等方差非正态总体均值相等性检验的单向ANOVA检验统计量T的零分布。在这种情况下，有几种检验统计量，特别地，我们只考虑James（1951）提出的这一检验统计量。当q个总体的样本容量都很大时，T的零分布收敛于。在一般条件下，我们推广了这个结果，得到了一个渐近展开式。为了计算这种展开式，我们使用了Fujikoshi，Ohmae and Yanagihara（1999）中的类似方法，并研究了基于极限分布和渐近展开式的T的当前点和实际测试大小的近似值的数值精度。
This paper deals with the null distribution of one-way ANOVA test statistic T for testing the equality of means of q nonnormal populations with unequa variances. In thwis situation , there are several test statistics Specially, we consider just this one which has been proposed by James(1951). It is known that the null distribution of T converges to when all the sample sizes from the q populations are large. we extend this result by obtaining an asymptotic expansion under a general condition. In order to calculate this expansion, we use a similar method in Fujikoshi, Ohmae and Yanagihara(1999).Numerical accuracies are studied for approximations of the precent points and actual test sizes of T based on the limiting distribution and an asymptotic expansion.