Characterization of a Ranked-Set Sample with Application to Estimating Distribution Functions

Distribution function estimation using concomitant-based ranked set sampling

“…The properties ofF RSS (t) have been studied by Stokes and Sager [11]. They proved that this estimator is unbiased and has less variance than empirical distribution function (EDF) in SRS of the same size, regardless of the quality of ranking.…”

“…Furthermore, they showed that the efficiency ofȲ RSS toȲ SRS is maximized when the population distribution is uniform. Stokes and Sager [11] considered the problem of estimating the cumulative distribution function (CDF), and proved that RSS CDF estimator is more efficient than its counterpart in SRS regardless of the ranking quality. Stokes [10], MacEachern et al [7] and Zamanzade and Vock [16] proposed some variance estimators based on a ranked set sample.…”

Some nonparametric tests of perfect judgment ranking for judgment post stratification

“…Virtually all of the most important and practical statistical problems are well addressed in the RSS literature. For example, the problem of estimation of a distribution function has been considered by Stokes and Sager (1988), Kvam and Samaniego (1994), and Duembgen and Zamanzade (2013). Stokes (1980), MacEachern et al (2002), Perron and Sinha (2004) and Zamanzade and Vock (2015) considered the problem of nonparametric estimation of variance.…”

Improved Estimation from Ranked Set Sampling

“…The RSS mean is at least as precise as the sample mean of the simple random sampling with replacement (SRSWR) sampling scheme of the same size. Stokes ( , 1980aStokes ( , 1988 showed that RSS provides precise estimators for cumulative distribution function, population variance and correlation coefficient.…”