Asymptotic Expansion for the Null Distribution of the <Emphasis Type="Italic">F</Emphasis>-statistic in One-way ANOVA under Non-normality |
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Authors: | Solomon W Harrar Arjun K Gupta |
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Institution: | (1) Department of Mathematics and Statistics, South Dakota State University, Brookings, SD 57007, USA;(2) Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA |
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Abstract: | In this paper we derive the asymptotic expansion of the null distribution of the F-statistic in one-way ANOVA under non-normality. The asymptotic framework is when the number of treatments is moderate but
sample size per treatment (replication size) is small. This kind of asymptotics will be relevant, for example, to agricultural
screening trials where large number of cultivars are compared with few replications per cultivar. There is also a huge potential
for the application of this kind of asymptotics in microarray experiments. Based on the asymptotic expansion we will devise
a transformation that speeds up the convergence to the limiting distribution. The results indicate that the approximation
based on limiting distribution are unsatisfactory unless number of treatments is very large. Our numerical investigations
reveal that our asymptotic expansion performs better than other methods in the literature when there is skewness in the data
or even when the data comes from a symmetric distribution with heavy tails. |
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Keywords: | Analysis of variance Edgeworth expansion Cumulants Characteristic function Asymptotic expansion Non-normality |
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