Pitman closeness results concerning ranked set sampling

We first compare the ranked set sampling (RSS) and simple random sampling schemes for the estimation of the population median through Pitman’s measure of closeness. Then, by using Banks’ criterion, we determine the frequency with which an individual order statistic is closer to the median than some symmetric estimator in an ϵ-neighbourhood of the median. Finally, we consider the simultaneous Pitman closeness criterion and identify the median RSS as the optimal RSS scheme for estimating the population median.