Comparing Non-Nested Linear Models

Abstract

Abstract I consider the usual linear-model situation, except that there are two possible linear subspaces that may contain the true mean vector, and neither of the two subspaces is nested within the other. Approximate confidence intervals are developed for the difference in mean squared error (MSE) of prediction using the two models, not assuming that either model is necessarily correct. The confidence intervals are based on parametric bootstrap methods, applied to Mallows's Cp estimate of the difference in MSE. This approach is shown to relate closely to Hotelling's test comparing two simple linear regressions. In the simplest case the problem is equivalent to finding a confidence interval for the product of the means of two independent normal observations, each with variance one.