12/01/1996 09:00 AM
Computer Engineering
Suppose Nature picks a probability measure P on a complete separable metric space X at random from a fixed set of probability measures. Then, without knowing which measure is picked, a statistician picks a measure Q on X. Finally, the statistician suffers a loss equal to the relative entropy between P 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, and Davisson and Leon-Garcia.
