Comparison of confidence intervals for variance components with unbalanced data

We compare the performance of three easily-computed confidence intervals for functions of variance components in the one-way random effect model. The confidence intervals are studied for three underlying generating distributions and a variety of sample sizes and degrees of unbalancedness. Confidence intervals based on the asymptotic covariance matrix for maximum likelihood estimates of the parameters perform poorly for small sample sizes for any function of the between variance component, regardless of the underlying distribution of the random effects.