Inconsistency of the MDL: On the performance of model order selection criteria with increasing signal-to-noise ratio
Date of Original Version
In the problem of model order selection, it is well known that the widely used minimum description length (MDL) criterion is consistent as the sample size N → ∞. However, the consistency as the noise variance σ2 → 0 has not been studied. In this paper, we find that the MDL is inconsistent as σ2 → 0. The result shows that the MDL has a tendency to overestimate the model order. We also prove that another criterion, the exponentially embedded family (EEF), is consistent as σ2 → 0. Therefore, in a high signal-to-noise (SNR) scenario, the EEF provides a better criterion to use for model order selection. © 2011 IEEE.
IEEE Transactions on Signal Processing
Ding, Quan, and Steven Kay. "Inconsistency of the MDL: On the performance of model order selection criteria with increasing signal-to-noise ratio." IEEE Transactions on Signal Processing 59, 5 (2011): 1959-1969. doi:10.1109/TSP.2011.2108293.