Title :
A general minimax result for relative entropy
Author_Institution :
Dept. of Comput. & Inf. Sci., California Univ., Santa Cruz, CA, USA
fDate :
7/1/1997 12:00:00 AM
Abstract :
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)
Keywords :
Bayes methods; entropy; game theory; minimax techniques; probability; sequential estimation; Bayes strategies; closure; complete separable metric space; game; general minimax result; maximin values; measurable set; minimax values; probability measure; relative entropy; sequential estimation game; Channel capacity; Entropy; Estimation theory; Extraterrestrial measurements; Loss measurement; Minimax techniques; Probability; Source coding; Statistical distributions;
Journal_Title :
Information Theory, IEEE Transactions on
