Simultaneous Selection of Extreme Populations: A Subset Selection Approach
Satya Narayan Mishra, Edward J. Dudewicz · Biometrical Journal · 1987
Abstract The problem of selecting a “best” (largest mean, or smallest mean) population from a collection of k independent populations was formulated and solved by Bechhofer (1954). Gupta (1965) solved another important problem, that of selecting a subset of populations containing the “best” population from the original collection of populations. Since then many variations of the problem have been considered. Tong (1969) and Lewis (1980) have investigated the problem of selecting extreme populations (populations with a largest, and populations with a smallest, mean) with respect to one and two standard populations, respectively. In this paper we study the selection of extreme populations in absence of any standard population. We formulate subset‐selection procedures when variances are known and equal, and also in the most general case when they are unknown and unequal. Nonexistence of a single‐stage procedure is noted for this latter case (even if variances are equal). A two‐stage procedure and some of its associated properties are discussed. Tables needed for application are provided, as is a worked example.