Discussion: Inference and Interpretability Considerations in Frequentist Model Averaging and Selection
Hjort and Claeskens are to be congratulated for addressing several important yet controversial issues on model averaging and selection. In these two stimulating articles, the authors advocated frequentist model averaging and provided the necessary asymptotic analyses to demonstrate its consistency as well as developed the focused information criterion (FIC) for guiding the model selection process. In our opinion model averaging and model selection as well as their associated inferential aspects are important in both statistical theory and practice. Although well studied, there are important yet subtle differences in the application of these approaches to model development and these deserve more attention. In this discussion we shall focus on the following aspects: (1) model interpretability, (2) model performance as measured by loss and risk, and (3) aspects of model-based inference. We shall provide a simple example for illustration of these points.