Generating subsets of order statistics with applications to trimmed means and means of trimmings

Abstract

This paper is concerned with the generation of subsets of order statistics from a uniform (U/(0,1)) population. In the first part of the paper two new methods for generating subsets of either central or extreme order statistics are given. They are based on an extension of the method by Ramberg and Tadikamalla (1978) used to generate the central order statistics. One of the new methods also utilizes a method for generating sequential order statistics given by Lurie and Hartley (1972). The second part of the paper deals with a specific application of generating the central or extreme order statistics, namely, the computation of a trimmed mean or mean of trimmings. When such estimates of location are required it is not necessary that the subsample be in precise order, since averaging gives equal weight to all (retained) observations. With this application substantial computer time can be saved by using one of the new methods proposed here.