21 ML ESTIMATORS FOR MODEL SELECTION

Classical approaches to determine a suitable model structure from obse rved input-output data are based on hypothesis tests and information-b ased criteria. Recently, the model structure has been considered as a stochastic variable, and standard estimation techniques have been prop osed. The resulting estimators are closely related to the aforemention ed methods. However, it turns out that there are a number of prior cho ices in the problem formulation, which are crucial for the estimators' behavior. The contribution of this paper is to clarify the role of th e prior choices, to examine a number of possibilities and to show whic h estimators are consistent. This is done in a linear regression frame work. For autoregressive models, we also investigate a novel prior ass umption on stability, and give the estimator for the model order and t he parameters themselves.