Asymptotic expansion of the null distribution of test statistic for linear hypothesis in nonnormal linear model |
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Authors: | Hirokazu Yanagihara |
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Affiliation: | Department of Statistical Methodology, Division of Multidimensional Analysis, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan |
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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 χ2 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. |
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Keywords: | Analysis of variance Asymptotic expansion Cornish– Fisher expansion Linear hypothesis Linear model Nonnormality Null distribution One-way ANOVA test Two-way ANOVA test |
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