Frequentist model average estimators

doi:10.1198/016214503000000828

2003-12-01

534

Nils Lid Hjort

Gerda Claeskens

DOI：10.1198/016214503000000828

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摘要

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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 where only a few crucial quantities matter. In particular, we offer a frequentist view on Bayesian model averaging methods and give a link to generalized ridge estimators. Our work also leads to new model selection criteria. The methods are illustrated with real data applications.

Keyword:

bias and variance balance

growing models

likelihood inference

model average estimators

model information criteria

moderate misspecification