Fiducial Generalized Pivots for a Variance Component vs. an Approximate Confidence Interval

Abstract. The paper is devoted to comparison of different confidence intervals for a variance component corresponding to the random factor in mixed linear models with two variance components. Namely, generalized confidence intervals (based on fiducial generalized pivots (FGP), see Hannig et al. (2006)) are compared to an approximate solution suggested by El-Bassiouni (1994). We focus on FGPs of certain types that were shown to yield exact intervals in some limiting situations. This makes them more equivalent counterparts to the El-Bassiouni’s interval, if frequentist properties are the main concern. A simulation study is presented that reveals, how besides sharing the limiting properties, these FGPs and the mentioned approximate interval perform with respect to each other. We also comment on a relationship between the considered types of FGPs.