Inconsistency of the MDL: On the performance of model order selection criteria with increasing signal-to-noise ratio
Document Type
Article
Date of Original Version
5-1-2011
Abstract
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.
Publication Title, e.g., Journal
IEEE Transactions on Signal Processing
Volume
59
Issue
5
Citation/Publisher Attribution
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.