An Asymptotically Optimal Sequential Design for Comparing Several Experimental Categories with a Control

Abstract

The basic problem is to decide none of $k$ experimental categories is better than the control or decide a certain category is better. For this problem three sequential procedures are examined with specification of how procedures are carried out in practice. With a definite loss function and a cost $c > 0$ per observation the three sequential procedures and fixed sample size procedures are compared in a certain asymptotic sense as $c \rightarrow 0$. In particular, one of the procedures is shown to be optimal in this asymptotic sense. By appealing to asymptotic results a discussion of the relative merits of the three sequential procedures as considered in practice is given.