High-SNR model order selection using exponentially embedded family and its applications to curve fitting and clustering

The exponentially embedded family (EEF) of probability density functions was originally proposed in [1] for model order selection. The performance of the original EEF deteriorates somewhat when nuisance parameters are present, especially in the case of high signal-to-noise ratio (SNR). Therefore, we propose a new EEF for model order selection in the case of high SNR. It is shown that without nuisance parameters, the new EEF is the same as the original EEF. However, with nuisance parameters, the new EEF takes a different form. The new EEF is applied to problems of polynomial curve fitting and clustering. Simulation results show that, with nuisance parameters, the new EEF outperforms the original EEF and Bayesian information criterion (BIC) at high SNR.