Multistage ranked set sampling

The superiority of using ranked set sampling, for estimating the mean of a population, over simple random sampling, is well established. This technique is useful when visual ordering of a small set of size (m) can be done easily and fairly accurately, but exact measurement of an observation is difficult and expensive. It is noted that for many distributions, an increase in the efficiency of ranked set sampling can be achieved by increasing the set size m. However, in practice, m should be kept very small so that visual ranking errors will not destroy the gain in efficiency. In this paper, multistage ranked set sampling is considered as a generalization of ranked set sampling, that results in an increase of the efficiency for fixed value of m. Steady state efficiency, the limiting efficiency as the number of stages approaches infinity, varies from one distribution to another. It is shown that this efficiency is always larger than 1, close to m² for symmetric distributions and equal to m² for the uniform distribution. Some real applications of the technique are discussed. Data on olive yield of olive trees is collected to illustrate the technique.