Testing of multialternative hypothesis under a priori uncertainty (Q1179609)

A statistical decision problem with finite sets of parameters and decisions is considered. It is assumed that prior distributions belong to a given subset of distributions on the parameter set. Randomized decision procedures, which yield a minimax value to the deviation of average risk from Bayes risk for a given prior distribution, are considered as optimal. Conditions of optimality for the decision procedure and the least favorable prior distributions are given for this problem. A special case when the set of prior distributions is a polyhedron is investigated. In this case the conditions of optimality are transformed to a finite set of simultaneous equations and inequalities. Some examples of application problems and their solutions are given.