Geodesic
A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models
Kybernetika, Tome 43 (2007) no. 4, pp. 471-480

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We consider a construction of approximate confidence intervals on the variance component $\sigma ^2_1$ 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 $\sigma ^2_1/\sigma ^2,$ was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when $\sigma ^2_1/\sigma ^2\rightarrow \infty $ suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when $\sigma ^2_1/\sigma ^2\rightarrow \infty .$ It turns out that this modification is an interval suggested by El-Bassiouni in [eb]. We comment on its properties that were not emphasized in the original paper [eb], but which support use of the procedure. Also a small simulation study is provided.
Classification : 62F25, 62J10
Keywords: variance components; approximate confidence intervals; mixed linear model 
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     author = {Arendack\'a, Barbora},
     title = {A modification of the {Hartung-Knapp} confidence interval on the variance component in two-variance-component models},
     journal = {Kybernetika},
     pages = {471--480},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2007},
     mrnumber = {2377925},
     zbl = {1134.62018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_4_a7/}
}
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Arendacká, Barbora. A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models. Kybernetika, Tome 43 (2007) no. 4, pp. 471-480. http://geodesic.mathdoc.fr/item/KYB_2007__43_4_a7/