Cautionary note on unbalanced ranked-set sampling
Balanced ranked-set sampling (RSS) offers improved statistical inference in situations where the units to be sampled can be ranked relative to each other prior to formal measurement. Recent work has shown that provided the ranking process is perfect, unbalanced RSS can do even better. In this article, we examine the performance of one unbalanced RSS technique when the ranking process is not perfect. Using an Ohio corn production data set, we show that median-based unbalanced RSS outperforms balanced RSS in estimating a population median if the rankings are nearly perfect. We also show, however, that median-based unbalanced RSS may perform extremely poorly when the ranking process is less than perfect. This effect is particularly pronounced when the variable of interest has a skewed distribution. We thus offer a note of caution for users of unbalanced RSS.
median-based unbalanced ranked-set samples concomitant ranking conditional probability distributions simple random sampling simulation study