On the choice of a discrepancy functional for model selection

Abstract

Consider the problem of several mathematical models competing to explain an empirical phenomenon. it is argued that fundamental model selection questions of model discrimination, model correctness and model adequacy can be answered by measuring the discrepancy of each model from an estimate of the unknown data generating process. Formally, the framework adopted is that of Linhart and Zucchini (1986), who considered a very general definition of discrepancy. In the present paper, it is demonstrated that requiring a discrepancy to possess several very reasonable properties is in fact equivalent to requiring it to be a metric on the relevant space of probability distributions.

Keywords:

• Model selection
• model discrimination
• discrepancy functional
• minimum distance estimation
• robustness
• principle of parsimony