Asymptotic expansion of the null distribution of test statistic for linear hypothesis in nonnormal linear model
Asymptotic expansion of the null distribution of test statistic for linear hypothesis in nonnormal linear model
复制标题
非正态线性模型线性假设检验统计量零分布的渐近展开
DOI：
10.1016/s0047-259x(02)00049-0
复制
发表时间：
2003
影响因子：
1.6
通讯作者：
H. Yanagihara
中科院分区：
文献类型：
--
作者：
H. Yanagihara
本文研究了线性模型中检验统计量T的零分布，在不假设正态误差的情况下，检验统计量T的零分布。检验统计量包括典型的ANOVA检验统计量。在设计矩阵满足一定条件的情况下，当样本容量n较大时，T的零分布收敛于χ 2。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。其次，利用这个一般的统计量，得到了单向和双向检验统计量的渐近展开式。基于极限分布和渐近展开式，研究了双因素方差分析检验案例T的百分点和实际检验规模的一些近似值的数值精度。
This paper is concerned with the null distribution of test statistic T for testing a linear hypothesis in a linear model without assuming normal errors. The test statistic includes typical ANOVA test statistics. It is known that the null distribution of T converges to χ2when the sample size n is large under an adequate condition of the design matrix. We extend this result by obtaining an asymptotic expansion under general condition. Next, asymptotic expansions of one- and two-way test statistics are obtained by using this general one. Numerical accuracies are studied for some approximations of percent points and actual test sizes of T for two-way ANOVA test case based on the limiting distribution and an asymptotic expansion.