Inconsistency of the MDL: On the Performance of Model Order Selection Criteria With Increasing Signal-to-Noise Ratio

Author

Ding, Quan ; Kay, Steven

Author_Institution

Dept. of Electr. Comput. & Biomed. Eng., Univ. of Rhode Island, Kingston, RI, USA

Volume

59

Issue

5

fYear

2011

fDate

5/1/2011 12:00:00 AM

Firstpage

1959

Lastpage

1969

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.

Keywords

signal processing; exponentially embedded family; minimum description length criterion; model order selection problem; noise variance; signal-to-noise scenario; Biological system modeling; Computational modeling; Gaussian noise; Materials; Signal to noise ratio; Testing; Consistency; exponentially embedded families; hypothesis testing; minimum description length; model order selection;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2011.2108293

Filename

5701798