The AIC-BIC dilemma: An in-depth look
Y. Song (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Jakob Söhl – Mentor (TU Delft - Statistics)
FH Van Der Meulen – Coach (TU Delft - Statistics)
EM van Elderen – Coach (TU Delft - Mathematical Physics)
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Abstract
In research there is often a need to choose between multiple competing models. Two popular criteria for model selection are the AIC and BIC. The AIC excels in estimating the best model for the unknown data generating process. The BIC on the other hand is consistent in finding the true model. It is clear that for model selection these two information criterion give answers to different selection criteria. The question that arises is whether it is possible to construct a model selection criterion which combines the strengths of both AIC and BIC. In this study we will show that it is impossible to construct a model selection criterion which shares the above mentioned two strenghts by revisiting the proof of \cite{yang2005can} : That is, any consistent model selection criterion must be sub-optimal in the minimax convergence rate for regression estimation compared to the AIC.