Optimality criteria for the selection of a partially sequential indicator set

Wolfe (1977a) introduced the concept of a partially sequential two-sample hypothesis test and studied some of the properties for a general class of such procedures. In this paper we deal with criteria for selecting an indicator set for use in a partially sequential test. In particular, we show how the Neyman-Pearson lemma can be used to generate an asymptotically optimal indicator set, in the sense that it corresponds to an asymptotically most powerful partially sequential test. In addition, we provide an accurate upper bound for the asymptotic expected sample size of the sequentially obtained observations, and obtain a closed form approximation for the maximum number of these observations necessary in order to obtain prespecified asymptotic power bounds against alternatives of interest