A theoretically founded over-penalization of the AIC criterion.

Summary The fact that a slight over-penalization leads to a stabilization of model selection procedures is a phenomenon well known by specialists. Indeed, it has been noticed since the end of the 70's that adding a small positive quantity to classical penalized criteria such as AIC improves in good cases the prediction results, especially for small or moderate sample sizes. The main reason is that over-penalization tends to guard against over-learning. We propose the first general and theoretically sound over-penalization strategy and apply it to the AIC criterion. Very good results are observed by simulation.