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Approximate interval for the between-group variance under heteroscedasticity. (English) Zbl 1431.62303
Summary: The paper presents an approximate confidence interval for the between-group variance in a one-way heteroscedastic random-effects model. Derivation of the interval is inspired by the ideas in [J. S. Williams, Biometrika 49, 278–281 (1962; Zbl 0138.13101)] for the homoscedastic case. Simulations suggest that the proposed interval performs better than or comparably to the other available procedures as studied in [G. Wimmer and V. Witkovský, J. Stat. Comput. Simulation 73, No. 5, 333–346 (2003; Zbl 1054.62026); J. Hartung and G. Knapp, J. Stat. Plann. Inference 127, No. 1–2, 157–177 (2005; Zbl 1083.62062); X. Li, Commun. Stat., Simulation Comput. 36, No. 2, 381–390 (2007; Zbl 1118.62037)]. Moreover, it is relatively easy to compute.
MSC:
62J10 Analysis of variance and covariance (ANOVA)
62F25 Parametric tolerance and confidence regions
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[1] DOI: 10.1080/0094965021000038940 · Zbl 1054.62026 · doi:10.1080/0094965021000038940
[2] DOI: 10.1016/j.jspi.2003.09.032 · Zbl 1083.62062 · doi:10.1016/j.jspi.2003.09.032
[3] DOI: 10.1080/03610910601158450 · Zbl 1118.62037 · doi:10.1080/03610910601158450
[4] Williams J. S., Biometrika 49 pp 278– (1962)
[5] DOI: 10.1080/03610929408831364 · Zbl 0825.62194 · doi:10.1080/03610929408831364
[6] DOI: 10.2307/2529647 · Zbl 0286.62055 · doi:10.2307/2529647
[7] DOI: 10.2307/2531641 · Zbl 0715.62073 · doi:10.2307/2531641
[8] Arendacká B., Kybernetika 43 pp 471– (2007)
[9] DOI: 10.1198/016214504000001682 · Zbl 1055.62124 · doi:10.1198/016214504000001682
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