Robust Akaike’s Criterion for Model Order Selection

Abstract

The paper considers the model order selection (Output Error model) of the system with constant parameters. Ad hoc selection of model order leads to overparametrization or parsimony problem. To avoid these problems, different selection criterions of the model are used: AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion) and FPE (Final Prediction Error Criterion). In this paper, Akaike's criterion is used, which is obtained by minimization of the Kullback-Leibler information distance. The criterion is basically a generalization of the maximum likelihood method. It is assumed that the stochastic disturbance in the model belongs to the class of ε-contaminated distributions. In such conditions the originally proposed AIC criterion cannot be applied. By determining the least favourable probability density for a given class of probability distribution represents a base for design of the robust version of AIC criterion. Simulations illustrate the behavior of the proposed criterion.