A note on model uncertainty in linear regression

We consider model selection uncertainty in linear regression. We study theoretically and by simulation the approach of Buckland and co-workers, who proposed estimating a parameter common to all models under study by taking a weighted average over the models, using weights obtained from information c...

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Bibliographic Details
Published inJournal of the Royal Statistical Society. Series D (The Statistician) Vol. 52; no. 2; pp. 165 - 177
Main Authors Candolo, C., Davison, A. C., Demétrio, C. G. B.
Format Journal Article
LanguageEnglish
Published Oxford, UK Blackwell Publishing 01.01.2003
Blackwell Publishers
Subjects
Akaike information criterion
Bayes information criterion
Bayesian networks
Bootstrap
Estimation bias
Estimators
Linear regression
Model averaging
Model uncertainty
Modeling
Parametric models
Prediction
Regression analysis
Statistical discrepancies
Statistical variance
Term weighting
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Summary:We consider model selection uncertainty in linear regression. We study theoretically and by simulation the approach of Buckland and co-workers, who proposed estimating a parameter common to all models under study by taking a weighted average over the models, using weights obtained from information criteria or the bootstrap. This approach is compared with the usual approach in which the 'best' model is used, and with Bayesian model averaging. The weighted predictor behaves similarly to model averaging, with generally more realistic mean-squared errors than the usual model-selection-based estimator.
Bibliography:ark:/67375/WNG-6TXWHMF4-Q
istex:20E15CBA6AF289098030F17EAB77138CD542DD56
ArticleID:RSSD349
ISSN:0039-0526
1467-9884
DOI:10.1111/1467-9884.00349