An Asymptotically Optimal Fixed Sample Size Procedure for Comparing Several Experimental Categories with a Control

Abstract

The basic problem considered here involves $k$ experimental categories. The experimenter must decide none of the $k$ categories is better than the control or decide a certain category is better. For this problem a fixed sample size procedure $\delta^\ast_m$ is given. With a definite loss function and a cost $c > 0$ per observation, $\delta^\ast_m$ and other fixed sample size procedures are compared in a certain asymptotic sense as $c \rightarrow 0$. In particular, $\delta^\ast_m$ is shown to be an optimal fixed sample size procedure in this asymptotic sense. By appealing to asymptotic results the procedure $\delta^\ast_m$ is compared with sequentially designed procedures.