Аннотация:We consider the following game of a statistician against the nature.
First the nature chooses a measure P at random from a measurable set P of Borel
probability measures on a complete separable metric space X. Then, without knowing
the strategy of the nature, the statistician chooses a Borel probability measure
Q on X. The loss of the statistician is the f-divergence J_f (P|Q). We show that
the minimax and maximin values of this game coincide and there always exists a
minimax strategy. This generalizes a result of Haussler proved for the case where
the loss is the Kullback–Leibler divergence D(P||Q).