Model Estimation and Classification Via Model Structure Determination

In model estimation, we often face problems with unknown parameters in the candidate models. This paper proposes the model structure determination (MSD) for model estimation with unknown parameters. We start with the problem of model order selection and decompose the probability density function (PDF) into the information provided by the data about the model parameters and that of the model structure. The factor that depends on the model parameters is approximated using a minimax procedure, and the MSD depends on the model structure only. It is shown that the MSD is equivalent to the exponentially embedded family (EEF) for model order selection under some conditions. Finally, we apply the MSD to a classification problem where we have partial knowledge about the parameters, and simulation results show that it outperforms the pseudo-maximum-likelihood (pseudo-ML) rule.