Frequentist Model Average Estimators

The traditional use of model selection methods in practice is to proceed as if the final selected model had been chosen in advance, without acknowledging the additional uncertainty introduced by model selection. This often means underreporting of variability and too optimistic confidence intervals. We build a general large-sample likelihood apparatus in which limiting distributions and risk properties of estimators post-selection as well as of model average estimators are precisely described, also explicitly taking modeling bias into account. This allows a drastic reduction in complexity, as competing model averaging schemes may be developed, discussed, and compared inside a statistical prototype experiment…