Generalized confidence intervals on the variance component in mixed linear models with two variance components

Abstract

The paper deals with construction of confidence intervals for the variance component in the family of distributions using generalized p-values. Unfortunately, when W has more than two different eigen values, the nonuniqueness of the appropriate test variable occurs. This was illustrated by Zhou and Mathew [Zhou, L. and Mathew, T., 1994, Some tests for variance components using generalized p-values. Technometrics, 36, 394–402.] on an example of a generalized test variable dependent on positive constants c i and as Zhou and Mathew mentioned, it is not clear which test variable is preferred in this situation. In the paper, we make a choice of c i inspired by some known test statistics used for testing the nullity of . Also another test variable, which cannot be derived from Zhou’s and Mathew’s, is stated and all mentioned test variables are compared.