Lu, M. and Mizon, G.E.
Mutual encompassing and model equivalence. Southampton, UK, University of Southampton
(Discussion Papers in Economics and Econometrics 9702).
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This paper analyses the properties of mutual encompassing and its relationship to the KLIC equivalence between statistical models. It is shown that models are KLIC equivalent if and only if they are mutually encompassing and mutually Cox-encompassing. Further, within the exponential family encompassing implies Cox-encompassing and so mutual encompassing is necessary and sufficient for KLIC equivalence in this family. In addition, it is shown that mutual encompassing is transitive for models in the exponential family
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