Nonparametric subset selection procedure for location parameters

Abstract

In this paper we propose a nonparametric subset selection procedure for selecting a subset containing the best population assuming that the underlying populations differ only in their location parameters. The population which corresponds to the largest location parameter is labeled as the best population. This type of formulation is usually encountered in agriculture, engineering, business etc. In agriculture, when variation in yield of all the varieties of a crop is same, the aim is to select those varieties which provide largest average yield for recommendation to the farming community. Similarly a business concern using different advertising methods to enhance the sales prefers those advertising methods with largest average sales among the methods having the same variability in sales. The proposed procedure is shown to satisfy the P*-condition and have all the properties desired by any selection procedure. The proposed procedure includes some of the existing procedures as its members which do exist in the literature under similar settings.

Using multivariate techniques, the proposed procedure is compared with the existing procedures in terms of asymptotic relative efficiency (Pitman), with interesting results. The implementation of the proposed procedure is illustrated with the help of existing tables and the sample size sufficient for their implementation is determined using extensive simulation study.