Contributed paper Study on the penalty functions of model selection criteria

The aim of this paper is to study the penalty functions of the well-known model selection criteria, AIC, BIC, and KIC, which can unify their formulas as 2ˆlog 1 /, APIC p n called Adjusted Penalty Information Criterion. The appropriate value of for APIC has been found to reduce the probabilities of over- and underfitting and also to overcome the weak signal-to-noise ratio. The value of is selected based on four measurements: the probability of over- and underfitting, the signal-to-noise ratio, the probability of order selected, and the observed 2L efficiency. Performance of APIC is examined by theoretical and extensive simulation study. The theoretical results show that, the probability of overfitting tends to zero and the signal-to-noise ratio tends to strong if the value of tends to infinity. However, the simulation results show that, when the true model is weakly identifiable, the small value of gives a high probability of correct order being selected. But, if the true model is very difficult to detect, the observed 2L efficiency is a meaningful measurement than the probability of order selected. The observed 2L efficiency suggests the large value of causes the high efficiency of APIC which indicates that the correct model is also the closet model, except when the true model can be specified more easily and sample sizes are moderate to large, the