Improved Large-Sample Confidence Intervals for Ratios of Variance Components in Nonnormal Distributions

The confidence level of the usual interval for a ratio of variance components is contingent on normally distributed random variables. In this article we focus on confidence intervals for ratios of variance components in balanced one-way random effects models based on the large-sample properties of restricted maximum likelihood (REML) estimators. While this procedure does not require that the random variables be normally distributed, one must estimate a parameter that is a function of the kurtosis of the underlying distributions. Simulation results indicate that REML-based confidence interval methods outperform other well-known methods in the majority of the cases considered.