A Non-Parametric Sequential Procedure for the Generalized Partition Problem

In selection and ranking, the partitioning of treatments by comparing them to a control treatment is an important statistical problem. For over eighty years, this problem has been investigated by a number of researchers via various statistical designs to specify the partitioning criteria and optimal strategies for data collection. Many researchers have proposed designs in order to generalize formulations known at that time. One such generalization adopted the indifference-zone formulation to designate the region between the boundaries for “good” and “bad” treatments as the indifference zone. Since then, this formulation has been adopted by a number of researchers to study various aspects of the partition problem. In this paper, a non-parametric purely sequential procedure is formulated for the partition problem. The “first-order” asymptotic properties of the proposed non-parametric procedure are derived. The performance of the proposed non-parametric procedure for small and moderate sample sizes is studied via Monte Carlo simulations. An example is provided to illustrate the proposed procedure.