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A general minimax result for relative entropy

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1 Author(s)
D. Haussler ; Dept. of Comput. & Inf. Sci., California Univ., Santa Cruz, CA, USA

Suppose nature picks a probability measure Pθ on a complete separable metric space X at random from a measurable set P Θ={Pθ:θ∈Θ}. Then, without knowing θ, a statistician picks a measure Q on S. Finally, the statistician suffers a loss D(P0||Q), the relative entropy between Pθ and Q. We show that the minimax and maximin values of this game are always equal, and there is always a minimax strategy in the closure of the set of all Bayes strategies. This generalizes previous results of Gallager(1979), and Davisson and Leon-Garcia (1980)

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IEEE Transactions on Information Theory  (Volume:43 ,  Issue: 4 )