Limit Solutions of Sequences of Statistical Games

Abstract

The present paper deals with the so-called “empirical Bayes approach” proposed and studied by Herbert Robbins. His papers, especially paper [3], have inspired us to show the notion of “empirical Bayes approach” fits into the framework of game theory by means of simple operations on games. We show it by examples of testing two simple statistical hypotheses (Example 5; the original version of this example was presented by H. Robbins in [3]). At the end we prove some easy lemmas concerning the relations between Bayes, minimax and limit solutions.