Encompassing
Formulation, Properties and Testing
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This monograph is a contribution to the theory of encompassing. It formalizes the idea that a model should be able to explain the result to obtained by other, rival models. From the properties of the encompassing relation established here, it follows that encompassing can be used as a simplifying device in empirical model buiding. As concerns statistical inference, encompassing is shown to induce the robust approach towards parametric inference, and to unify the theories of nested and non-nested hypotheses testing.
The history of many sciences is characterized by an almost continuous emer gence of new theories. From a normative point of view, the survival of a new theory should mainly be determined by its ability to explain a new body of facts which the existing theories are unable to explain. If in addition the new theory is able to explain all the results obtained by the existing theories and if it can point out why these theories fail to explain certain facts, it should become the dominant theory. Otherwise, it might coexist with other theories for some time. Hence, a new theory ought to be judged not only by confronting it with existing facts, but also by confronting it with existing theories. The idea that a theory should be able to account for the results ob tained by other theories, although implicitly adhered to by many scientists, has rarely been formalized. The statistics literature on parametric hypoth esis testing, though, might be seen as an instance of such a formalization.
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