On the Distributional Properties of Model Selection Criteria

Abstract It is commonly accepted that statistical modeling should follow the parsimony principle; namely, that simple models should be given priority whenever possible. But little quantitative knowledge is known concerning the amount of penalty (for complexity) regarded as allowable. We try to understand the parsimony principle in the context of model selection. In particular, the generalized final prediction error criterion is considered, and we argue that the penalty term should be chosen between 1.5 and 5 for most practical situations. Applying our results to the cross-validation criterion, we obtain insights into how the partition of data should be done. We also discuss the small sample performance of our methods.