Bruce E. Hansen

"Least Squares Model Averaging"

Econometrica, (2007), 75, 1175-1189.


This paper considers the problem of selection of weights for averaging across least-squares estimates obtained from a set of models. Existing methods for model averaging are based on exponential AIC and BIC weights. In distinction, this paper introduces a Mallows' criterion, which can be minimized to select the empirical model weights. This Mallows' criterion is an estimate of the average squared error from the model average fit. We show that our new Mallows' Model Average (MMA) estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators. In a simulation experiment we show that the MMA estimator compares favorably with those based on AIC and BIC weights. The proof of the main result is an application of Li (1987).

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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.