Frequentist Model Averaging and Focused Information Criteria

• Activity Number: 100
• Type: Invited
• Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
• Sponsor: JASA, Theory and Methods
• Author(s): Nils L. Hjort*+ and Gerda Claeskens
• Companies: University of Oslo and Texas A&M University
• Keywords: focused information criteria ; model averaging ; model selection

Abstract

The traditional use of model selection methods 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 confidence intervals that are too optimistic. 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 of complexity, as competing model averaging schemes may be developed, discussed, and compared within a statistical prototype experiment where only a few crucial quantities matter. In particular we offer a frequentist view on Bayesian model averaging methods and give a link to generalised ridge estimators. Our work also leads to new model selection criteria. These are focused, in the sense that they are geared towards the parameter singled out for attention, giving in particular different models for different focus parameters. Our methods are illustrated with real data applications.