Since the introduction of Akaike’s information criteria (AIC) in 1973, numerous information criteria have been developed and widely used in model selection. Many papers concerning the justification of various model selection criteria followed, particularly with respect to model selection error rates (the probability of selecting a wrong model). A model selection criterion is called consistent if the model selection error rate decreases to zero as the sample size increases to infinity. Otherwise, it is inconsistent. In this paper, we explore sufficient consistency conditions for information criteria in the nonparametric (logspline) and parametric model comparison setting, and discuss finite sample model selection error rates.
Digital Object Identifier: 10.1214/10-IMSCOLL612