Simultaneous confidence intervals for two estimable functions and their ratio under a linear model

This article considers the problem of finding simultaneous confidence intervals for two estimable functions of linear model parameters and their ratio. A pertinent example is the dominance ratio in crossing experiments with plants and animals, which is computed from an estimate of the dominance and additive gene effects. Breeders are usually interested in inferences on the ratio along with the effect estimates. We investigate several solutions to the problem. One proposal uses a plug-in approach, based on the multivariate-t distribution, which is shown by simulation to have good small-sample properties. A conservative method is proposed, which operates under a worst-case scenario. Both methods yield simultaneous coverage probabilities closer to the nominal level than the Scheffe or Bonferrom method. The methods are illustrated using two real examples, one from the Child Health and Development Studies and one from plant breeding. A small simulation study is performed to compare alternative approaches.