An application of ranked set sampling for mean and median estimation using USDA crop production data
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Ranked set sampling (RSS) is a sampling approach that leads to improved statistical inference in situations where the units to be sampled can be ranked (either through some subjective judgment or via the use of an auxiliary variable) relative to each other prior to formal measurement. It has the most promise for leading to improved methodology in situations where ranking of the items to be sampled can be carried out relatively easily and cheaply compared to the effort and expense required for actual quantification of the characteristic of interest. Although the theoretical benefits of RSS in estimation and statistical inference have been extensively demonstrated in the literature, the methodology has not yet been widely adopted by practitioners. The aim of this study is to use a crop production dataset from the United States Department of Agriculture to demonstrate the practical benefits of RSS relative to the more commonly used simple random sampling in estimation of the mean and median of a population. The results of our study provide clear evidence that the use of RSS can lead to substantial gains in precision of estimation for both of these situations.
Key WordsAuxiliary ranking variable Balanced ranked set sampling Concomitant ranking Set sizes Simple random sampling Simulation study
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