Estimating the Model Order in Exponential Families

We present a new approach to the problem of model order determination for probabilistic models from the exponential family. We suggest an order estimator which is optimal in the sense of minimizing the underestimation probability, while keeping the overestimation probability below a prescribed exponential level(generalizing the Neyman-Pearson criterion). The estimation is computationally inexpensive compared to existing methods. Several hypothesis testing problems can be easily solved as special examples of this model order estimation setup. The results generalize to models where more than on order is to be estimated (e.g., the ARMA(p,q) model), and to the estimation of the number of states of a finite-state source.