Abstract:We propose a nonparametric variance estimator when ranked set sampling (RSS) and judgment post stratification (JPS) are applied by measuring a concomitant variable. Our proposed estimator is obtained by conditioning on observed concomitant values and using nonparametric kernel regression.

The purpose of this study is to suggest a new modification of the usual ranked set sampling (RSS) method, namely; neoteric ranked set sampling (NRSS) for estimating the population mean and variance. The performance of the empirical mean and variance estimators based on NRSS are compared with their counterparts in ranked set sampling and simple random sampling (SRS) via Monte Carlo simulation. Simulation results revealed that the NRSS estimators perform much better than their counterparts using RSS and SRS designs when the ranking is perfect. When the ranking is imperfect, the NRSS estimators are still superior to their counterparts in ranked set sampling and simple random sampling methods. These findings show that the NRSS provides a uniform improvement over RSS without any additional costs. Finally, an illustrative example of a real data is provided to show the application of the new method in practice.

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Rank-based sampling methods are applicable in settings where precise measurements are expensive, but small sets of units can be accurately ranked at negligible cost. This article introduces one such a design, called multistage pair ranked set sampling. It mitigates ranking burden associated with a competitor scheme, namely multistage ranked set sampling. The mean estimator in multistage pair ranked set sampling is unbiased, and under perfect rankings has variance no larger than its simple random sampling counterpart. Although the suggested mean estimator is outperformed by its multistage ranked set sampling analog in terms of precision under perfect rankings, the situation may be reversed if cost considerations are taken into account. The methodology is illustrated using a medical dataset.