A fiducial-based approach to the one-way ANOVA in the presence of nonnormality and heterogeneous error variances. (English) Zbl 07193804
Summary: In this study, we propose a new test for testing the equality of the treatment means in one-way ANOVA when the usual normality and the homogeneity of variances assumptions are not met. In developing the proposed test, we benefit from the Fisher’s fiducial inference [R. A. Fisher, Proc. Camb. Philos. Soc. 26, 528–535 (1930; JFM 56.1083.05); Proc. R. Soc. Lond., Ser. A 139, 343–348 (1933; JFM 59.1207.02); Ann. Eugenics, London, 6, 391–398 (1936; JFM 62.1345.02)]. Distribution of the error terms is assumed to be long-tailed symmetric (LTS) which includes the normal distribution as a limiting case. Modified maximum likelihood (MML) estimators are used in the test statistics rather than the traditional least squares (LS) estimators, since LS estimators have very low efficiencies under nonnormal distributions, see [M. L. Tiku, “Estimating the mean and standard deviation from a censored normal sample”, Biometrika 54, No. 1–2, 155–165 (1967; doi:10.1093/biomet/54.1-2.155)] for the details of MML methodology. An extensive Monte Carlo simulation study is done to compare the efficiency of the proposed test with the corresponding test based on normal theory, see [X. Li et al., Comput. Stat. Data Anal. 55, No. 5, 1993–2002 (2011; Zbl 1328.62098)]. Finally, we give a real life example to show the applicability of the proposed methodology.
MSC:
| 62-XX | Statistics |
Keywords:
one-way ANOVA; fiducial inference; long-tailed symmetric distribution; modified likelihood; Monte Carlo simulationReferences:
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