A Comparison study of a Information Criterion and Cox's Test in Non-Nested Models

AIC is commonly used for model selection but the value of AIC has no direct interpretation Cox's test is a generalization of the likelihood ratio test When the true model is unknown based on AIC we select a model but we cannot talk about the closeness of the selected model to the true model Because it is not clear the selected model is wellspecified or mis-specified This paper extends Akaikes AIC-type model selection beside the Cox test for model selection and based on the simulations we study the results of AIC and Cox's test and the ability of these two criterion and test to discriminate models If based on AIC we select a model whether or not Cox's test has a ability of selecting a better model Words which one will considering the foundations of the rival models On the other hand the model selection literature has been generally poor at reflecting the foundations of a set of reasonable models when the true model is unknown As a part of results we will propose an approach to selecting the reasonable set of models.