Informational Complexity Criteria For Regression Models.

This paper pursues three objectives in the context of multiple regression models: 1) To give a rationale for model selection criteria which combine a badness of fit term (such as minus twice the log likelihood) with a measure of complexity of a model. 2) To investigate the asymptotic consistency properties of the class of ICOMP criteria first in the case when one of the models considered is the true model and to introduce and establish a consistency property for the case when none of the models is the true model. 3) To investigate the finite sample behavior of ICOMP criteria by means of a simulation study where none of the models considered is the true model.