Constrained nonparametric estimation of the mean and the CDF using ranked-set sampling with a covariate

Abstract

Ranked-set sampling (RSS) and judgment post-stratification (JPS) are related schemes in which more efficient statistical inference is obtained by creating a stratification based on ranking information. The rankings may be completely subjective, or they may be based on values of a covariate. Recent work has shown that regardless of how the rankings are done, the in-stratum cumulative distribution functions (CDFs) must satisfy certain constraints, and we show here that if the rankings are done according to a covariate, then tighter constraints must hold. We also show that under a mild stochastic ordering assumption, still tighter constraints must hold. Taking advantage of these new constraints leads to improved small-sample estimates of the in-stratum CDFs in all RSS and JPS settings. For JPS, the new constraints also lead to improved estimates of the overall CDF and the population mean.

On estimating the area under the ROC curve in ranked set sampling

“…Because RSS allows us to achieve a precision level with a smaller sample size as compared with SRS. Nonparametric inference in RSS about the population mean, 2,3 and distribution function [4][5][6][7] has been studied recently. Some two-sample problems in this design have also been investigated.…”

Two-Layer Median Ranked Set Sampling

“…Dell and Clutter [7] as well as David and Levine [6] reported similar results under imperfect ranking, which means there is a ranking error. For some recent bibliography on the RSS, see [8,11,18,20].…”

Combining ranking information in judgment post stratified and ranked set sampling designs

“…This constraint is weaker than stochastic ordering restriction and leads to better estimators for population mean and CDF. Frey (2010) combined the tight constraint in Frey and Ozturk (2010) with the mild stochastic ordering constraint to show that more efficient inference is possible for overall CDF and population mean in JPS.…”