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A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models. (English) Zbl 1134.62018
Summary: We consider a construction of approximate confidence intervals on the variance components \(\sigma_1^2\) in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large \(\sigma_1^2/\sigma^2\), was considered by J. Hartung and G. Knapp [J. Stat. Comput. simulation 65, No. 4, 311–323 (2000; Zbl 0966.62044)]. The expression for its asymptotic coverage when \(\sigma_1^2/\sigma^2\to\infty\) suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when \(\sigma_1^2/\sigma^2\to\infty\). It turns out that this modification is an interval suggested by M. Y. El-Bassiouni [Commun. Stat., Theory Methods 23, No. 7, 1915–1933 (1994; Zbl 0825.62194)]. We comment on its properties that were not emphasized in the original paper of El-Bassiouni, but which support use of the procedure. Also a small simulation study is provided.
62F25 Parametric tolerance and confidence regions
62J10 Analysis of variance and covariance (ANOVA)
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