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Bayesian Averaging, Prediction and Nonnested Model Selection

  • Han Hong
  • Bruce Preston

This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models.

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File URL: http://www.nber.org/papers/w14284.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14284.

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Date of creation: Aug 2008
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Publication status: published as Hong, Han & Preston, Bruce, 2012. "Bayesian averaging, prediction and nonnested model selection," Journal of Econometrics, Elsevier, vol. 167(2), pages 358-369.
Handle: RePEc:nbr:nberwo:14284
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