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

✍ Scribed by Hirokazu Yanagihara

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
250 KB
Volume
84
Category
Article
ISSN
0047-259X

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✦ Synopsis

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 w 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.

πŸ“œ SIMILAR VOLUMES

An Asymptotic Expansion for the Distribu
An Asymptotic Expansion for the Distribution of Hotelling'sT2-Statistic under Nonnormality
✍ Yasunori Fujikoshi πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 630 KB

In this paper we obtain an asymptotic expansion for the distribution of Hotelling's T 2 -statistic T 2 under nonnormality when the sample size is large. In the derivation we find an explicit Edgeworth expansion of the multivariate t-statistic. Our method is to use the Edgeworth expansion and to expa