Statistica Sinica

Wolfgang Bischoff and Frank Miller

Abstract:We discuss a problem occuring when a new manufacturing process is investigated. For such applications, it is typical that the relationship among the input variables and the output variables is unknown. After obtaining information on this relationship by experiments, the goal is not only to make statistical inference on this relationship, but to come to a decision for a problem that depends upon it. In our context, the problem is to first test a certain hypothesis against an alternative and then to estimate a certain parameter in case the hypothesis is rejected. The main objective is to develop a solution for the problem as a whole, i.e., a solution of the joint test and estimation problem. We determine the optimal minimax procedure in a certain class by numerical integration. Moreover, we show that the optimal two-stage minimax procedure is better than the optimal one-stage minimax procedure.

Key words and phrases:Comparing treatments, decision theory, hybrid test and estimation problem, minimax procedure, two-stage procedure.