A short note on the j-minimax and mean-max risk functions
Résumé
In a recent paper [2], the authors hâve proved that the mean-max risk and the J-minimax risk coincide, where J is a specified class of probability measures and when a regularity condition (denotqji: as «nondition (c)) is fulfilled. Moreover, it was proved that this condition was not needed when the mean-max risk is associated with a subsigmafield generated by a countable partition of the abstract parametric space. In this paper we prove that condition (c) is also not needed for getting equality of J-minimax risk and mean-max risk, if some topological assumptions on the parametric space are imposed.
Domaines
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