The distance between regression models and its impact on model selection

In the case of nested hypothesis testing there exist many model selection criteria with which a “best” model is chosen. It is however very likely that the estimated hypotheses are all “incorrect”. In this paper model choice is made while assuming the existence of a “true” model. After the introduction of the distance as a measure of difference between models, it is demonstrated that model selection is influenced by the correct specification. Eight choice criteria are compared with respect to this influence.