Data-based decision theory under imprecise probability has to deal with optimisation problems where direct solutions are often computationally intractable. Using the $\Gamma$-minimax optimality criterion, the computational effort may significantly be reduced in the presence of a least favorable model. In 1984, A. Buja derived a neccessary and sufficient condition for the existence of a least favorable model in a special case. The present article proofs that essentially the same result is valid in case of general coherent upper expectations. This is done mainly by topological arguments in combination with some of L. Le Cam's decision theoretic concepts. It is shown how least favorable models could be used to deal with situations where the distribution of the data as well as the prior is assumed to be imprecise.
Keywords. Decision theory, robust statistics, imprecise probability, coherent upper expectations, Le Cam, equivalence of models, least favorable models
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Authors addresses:
Department of Statistics
LMU Munich
Ludwigstr. 33
D-80539 Munich
E-mail addresses:
| Robert Hable | Robert.Hable@stat.uni-muenchen.de |
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