Asymptotic expansion of the null distribution of test statistic for linear hypothesis in nonnormal linear model

JOURNAL OF MULTIVARIATE ANALYSIS

卷:84

Article

Yanagihara, H

关键词: analysis of variance;    asymptotic expansion;    Cornish-Fisher expansion;    linear hypothesis;    linear model;    normormality;    null distribution;    one-way ANOVA test;    two-way ANOVA test;   

DOI  :  10.1016/S0047-259X(02)00049-0

来源: Elsevier

【 摘 要 】

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 chi(2) when 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. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free