Blockwise AICc and its consistency properties in model selection
Abstract Akaike information criterion (AIC) and corrected Akaike information criterion (AICc) are two widely used information criteria. It is well known that neither of them is consistent because there is a positive probability to select an over-specified candidate model. In this paper, with the assumption that the sample size tends to be infinite, we derive the probability of the true model’s AICc (AIC) value less than an over-specified model’s AICc (AIC) value, and we also derive the lower bound of probability of selecting the true model using AICc (AIC) when the candidate model set includes all possible candidate models. We also prove that blockwise AICc, a new information criterion, is a consistent information criterion if the number of blocks and sample size both tend to be infinite. Furthermore, compared with the other popular information criteria, simulations and real data analysis also show that bAICc performs well for moderate and large sample sizes.