TY  - JOUR
AU  - Hong,Han
AU  - Preston,Bruce
TI  - Bayesian Averaging, Prediction and Nonnested Model Selection
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 14284
PY  - 2008
Y2  - August 2008
UR  - http://www.nber.org/papers/w14284
L1  - http://www.nber.org/papers/w14284.pdf
N1  - Author contact info:
Han Hong
Landau Economics Building
579 Serra Mall
Stanford, CA 94305
E-Mail: doubleh@stanford.edu

Bruce Preston
Department of Economics
Columbia University
420 West 118th Street
New York, NY 10027
Tel: 212/854-4092
Fax: 212/854-8059
E-Mail: bp2121@columbia.edu
AB  - 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.
ER  -