Model selection by cross-validation

The cross-validation principle is used to address the task of model selection. Assuming that a set of probabilistic models is given or constructed, the derivation of a selection rule via Bayesian predictive densities is discussed. A selection rule is derived for the set of nested normal linear regression models. Conditioned on the assumption that the true model is in the set of examined models, this rule asymptotically yields consistent selection of the true model. Some simulation results to demonstrate the performance of the selection criterion are included.