CDF estimation in multistage pair ranked set sampling

Abstract

Multistage pair ranked set sampling (MSPRSS) is a rank-based design that improves statistical inference with respect to simple random sampling of the same size. It is applicable when exact measurement is difficult, but judgment raking of the potential sample units can be done fairly accurately and easily. The ranking is usually performed based on personal judgment or a concomitant variable, and need not be totally free of errors. This article deals with estimating the cumulative distribution function in MSPRSS. The proposed estimator is theoretically compared with its contenders in the literature. The findings are supported by numerical evidence from simulation, and real data in the context of body fat analysis. Finally, a cost analysis is performed to show the advantage of the estimator.