Abstract
Approximation of parametric statistical models by exponential models is discussed, from the viewpoints of observed as well as of expected likelihood geometry. This extends a construction, in expected geometry, due to Amari. The approximations considered are parametrization invariant and local. Some of them relate to conditional models given exact or approximate ancillary statistics. Various examples are considered and the relation between the maximum likelihood estimators of the original model and the approximating models is studied.
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Research partly supported by the Danish Science Research Council.
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Barndorff-Nielsen, O.E., Jupp, P.E. Approximating exponential models. Ann Inst Stat Math 41, 247–267 (1989). https://doi.org/10.1007/BF00049394
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DOI: https://doi.org/10.1007/BF00049394