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

Hirokazu Yanagihara

Journal of Multivariate Analysis, 2003, vol. 84, issue 2, 222-246

Abstract: 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.

Keywords: Analysis; of; variance; Asymptotic; expansion; Cornish-Fisher; expansion; Linear; hypothesis; Linear; model; Nonnormality; Null; distribution; One-way; ANOVA; test; Two-way; ANOVA; test (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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