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The rules of conditional inference: Is there a universal definition of nonformation?

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All animals are equal, but some animals are more equal than others. From ‘Animal Farm’, by G. Orwell (1945).

Summary

We consider the ideas of sufficiency and ancillarity for parametric models with nuisance parameters, and more generally Barndorff-Nielsen's notion of nonformation. The original four definitions of non-formation, namelyB-,S-,G- andM-nonformation, each cover different types of models. We stress the interpretation of nonformation in terms of the idea of perfect fit. This leads to a new definition of nonformation, calledI-nonformation, which is well suited for inference in exponential families. We also consider Rémon's concept ofL-sufficiency, and a recent extension toL-nonformation, due to Barndorff-Nielsen, which unifies and extendsB-,S- andG- nonformation. We study the relations between these six definitions, and show that they are all special cases ofM-nonformation.

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  1. Department of Statistics, University of British Columbia, Vancouver, B.C., Canada

    Bent Jørgensen

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  1. Bent Jørgensen
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Jørgensen, B. The rules of conditional inference: Is there a universal definition of nonformation?. J. It. Statist. Soc. 3, 355–384 (1994). https://doi.org/10.1007/BF02589024

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