New estimator for the variances of strata in ranked set sampling

Ranked set sampling (RSS) utilizes imprecise rankings on the variable of interest in order to draw an informative sample from the target population. The resulting sample, consisting of independent judgment order statistics, resembles a stratified random sample. Estimating the variances of strata is an important problem in RSS. The standard method is based on the sample variance of units in each stratum. A plug-in estimator is also available in the literature that remedies some shortcomings of the standard estimator. We adjust the latter estimator using kernel estimator of the distribution function. The developed estimator is shown to be consistent, and its performance is investigated by means of simulation. It turns out that our proposal can be considerably more efficient than the existing estimators when perfect or nearly perfect ranking holds.