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It is common knowledge that the Akaike’s information criterion (AIC) is not a consistent model selection criterion. This inconsistency property has been confirmed from an asymptotic selection probability evaluated from a large-sample asymptotic framework. However, when a high-dimensional asymptotic framework, such that the dimension of the response variables and the sample size are approaching 1, is used for evaluating the selection probability, we can prove a consistency property of the AIC for selecting variables in multivariate linear models. This means that the probability of selecting the true model by the AIC goes to 1 as the sample size and the dimension simultaneously approach 1. The consistency property is also checked numerically by conducting a Monte Carlo simulation.

A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large