Blockwise AIC_c and its consistency properties in model selection

Abstract

Akaike information criterion (AIC) and corrected Akaike information criterion (AIC_c) 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 AIC_c (AIC) value less than an over-specified model’s AIC_c (AIC) value, and we also derive the lower bound of probability of selecting the true model using AIC_c (AIC) when the candidate model set includes all possible candidate models. We also prove that blockwise AIC_c, 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 bAIC_c performs well for moderate and large sample sizes.

Keywords:

• Model selection
• AICc
• bAICc
• consistency

MATHEMATICS SUBJECT CLASSIFICATION:

• 62-07

Acknowledgments

The authors are sincerely grateful to the editor, associate editor, and anonymous referees for their helpful comments and suggestions on the earlier version of this paper which lead to this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that support the findings of this study are openly available in Harvard Dataverse at https://doi.org/10.7910/DVN/3FEESF, Gelman and Hill (2006).

Additional information

Funding

This work was supported by the Scientific Research Foundation (doctor) of Jilin Jianzhu University (Grant No. 86123801).