On the behavior of information theoretic criteria for model order selection

The Akaike information criterion (AIC) and the minimum description length ( MDL) are two well-known criteria for model order selection in the additive white noise case. Our aim is to study the influence on their behavior of a large gap between the signal and the noise eigenvalues and of the noise eig envalue dispersion. Our results are mostly qualitative and serve to explain the behavior of the AIC and the MDL in some cases of great practical impor tance. We show that when the noise eigenvalues are not clustered sufficient ly closely, then the AIC and the MDL may lead to overmodeling by ignoring a n arbitrarily large gap between the signal and the noise eigenvalues, For f ixed number of data samples, overmodeling becomes more likely for increasin g the dispersion of the noise eigenvalues, For fixed dispersion, overmodeli ng becomes more likely for increasing the number of data samples. Undermode ling may happen in the cases where the signal and the noise eigenvalues are not well separated and the noise eigenvalues are clustered sufficiently cl osely. We illustrate our results by using simulations from the effective ch annel order determination area.