A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models

We consider a construction of approximate confidence intervals on the variance component σ 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 σ 2 1/ σ 2 , was considered by Hartung and Knapp in [6]. The expression for its asymptotic coverage when σ 2 1/ σ 2 → ∞ suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when σ 2 1/ σ 2 → ∞. It turns out that this modification is an interval suggested by El-Bassiouni in [5]. We comment on its properties that were not emphasized in the original paper [5], but which support use of the procedure. Also a small simulation study is provided.