9802358 Douglas A. Wolfe Ranked-set sampling is an approach to collecting data that has been shown to lead to substantial improvement over simple random sampling in the properties of statistical inference procedures for both the one-and two-sample settings. The development of nonparametric ranked-set sample procedures has been relatively recent in the literature and there is much yet to be completed. Such development is vital, however, since often the type of data for which measurement is difficult is also likely to be data which have a distribution that is not Gaussian. This research involves three major thrusts. First, the investigators study the all-important optimal choice of ranked-set judgment sample size, concentrating not only on the relative costs of measurements versus judgment orderings but also on the effect of imperfect judgment rankings on the entire process. In most cases, the optimization criterion is taken to be the Pitman asymptotic relative efficiency of the associated procedures. A second part of this research deals with the dual question of which order statistics should be measured in the ranked-set samples and then how best to differentially weight those that are measured. This portion of the study also investigates the potential gains from collecting more than a single order statistic from each judgment sample. Finally, the investigators extend nonparametric ranked-set sample procedures to other statistical problems, such as development of ranked-set sample analogs to the k-sample Kruskal-Wallis test and the Spearman and Kendall correlation procedures. In situations where measurements are costly and/or difficult to obtain but ranking of the potential sample data is relatively easy and accurate, the use of statistical methods based on a ranked-set sampling approach can lead to substantial improvement over analogous methods associated with more standard simple random sampling schemes. Ranked-set sampling utilizes information gained without formal measurement to provide more structure in the eventual measured data than is available in a corresponding simple random sample of the same size. This enables investigators to obtain the same information from fewer observations at less cost. This is particularly important in areas such as ecological and environmental studies where assessment of collected samples can be quite expensive or in medical studies where utilizing the additional judgment ranking in ranked-set sampling leads to fewer subjects involved in the development and testing of new medications or procedures prior to FDA approval. There is also tremendous potential for this sampling approach in economic predictions and auditing procedures, where the information of interest is often very time-consuming to collect and ranked-set sampling can help guide the search for those judgment ordered observations (fewer of them) which are best to quantify.
