A comparative study of model selection criteria for the number of signals

The performance of six existing model selection criteria is compared, which are commonly used in time series and regression analysis, when they are applied to the problem of the number of signals in the multiple signal classification (MUSIC) method. The five criteria are Akaike Information Criterion (AIC), Hannan and Quinn Criterion, Bayesian Information Criterion (BIC), Corrected AIC (AICc) and the recently introduced Vector Corrected Kullback Information Criterion (KICvc) and Weighted- Average Information Criterion (WIC). The general form of the above information criteria consists of a log likelihood function expressed in terms of the eigenvalues of the sample covariance matrix and a unique penalty term. In our estimation procedure, the number of signals is obtained by minimising each of the above criteria. Several simulated data sets, including a linear antenna array data set, are adopted for the comparison purpose. The authors show that, in simple MUSIC additive white noise model, for small sample size n, WIC performs nearly as well as AICc and outperforms other criteria, and for moderately large to large n, WIC performs nearly as well as BIC and outperforms other criteria. Therefore when the authors are not certain of the relative sample size, WIC may be a practical alternative to any criterion. The main purpose is to draw the attention and interests of signal processing researchers to adopt more recent statistical model selection criteria, such as WIC, in general signal processing problems.