BUREAU OF THE CENSUS STATISTICAL RESEARCH DIVISION REPORT SERIES SRD Research Report Number: CENSUS/SRD/RR-88/21 COMPARING NOT NECESSARILY NESTED MODELS WITH THE MINIMUM AIC AND THE MAXIMUM KULLBACK-LEIBLER ENTROPY CRITERIA: NEW PROPERTIES AND CONNECTIONS

Applied statistical modelers frequently have to compare models of rather w different forms. To the extent that objective criteria are used to facilitate such compatisons, Akaike’s minimum AIC criterion seems to be the one most widely used, due in part, perhaps, to its ease of use and its impressive successes in some industrial applications. A coherent theory to motivate MAIC’s use with non-nested model comparisons has been lacking, however, and the present paper seeks to describe one. Not surprisingly, Akaike’s non-operative Entropy Maximization Principle turns out to provide a model of what successful performance might mean in some subtle situations involving incorrect models. This paper summarizes some new results concerning this principle, a linear stochastic regression version of Akaike’s criterion, and the related criteria of Schwarz and Hannan and Quinn. Some analyses related to a successful ship autopilot design project are presented to illustrate the application of MAIC. Our theoretical results are directed towards analyzing the performance of the model selection criteria in some general situations, including three in which the preferred model, or lack of one, seems obvious a priori. Loosely described, these three situations are: