Model‐Averaged Confidence Intervals

We develop an approach to evaluating frequentist model averaging procedures by considering them in a simple situation in which there are two‐nested linear regression models over which we average. We introduce a general class of model averaged confidence intervals, obtain exact expressions for the coverage and the scaled expected length of the intervals, and use these to compute these quantities for the model averaged profile likelihood (MPI) and model‐averaged tail area confidence intervals proposed by D. Fletcher and D. Turek. We show that the MPI confidence intervals can perform more poorly than the standard confidence interval used after model selection but ignoring the model selection process. The model‐averaged tail area confidence intervals perform better than the MPI and postmodel‐selection confidence intervals but, for the examples that we consider, offer little over simply using the standard confidence interval for θ under the full model, with the same nominal coverage.