Variance estimation in ranked set sampling using a concomitant variable

Abstract

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.

New ranked set sampling for estimating the population mean and variance

“…Their estimator was obtained by conditioning on observed concomitant values and using nonparametric kernel regression. Zamanzade and Vock [22]'s simulation results indicated that their proposed estimator considerably improves the estimation of variance when the rankings are fairly good. However, since our interest here is not about using values of concomitant variable, we do not consider their estimator for more investigations.…”

“…They showed that this estimator is more efficient than S Another estimator of variance when the RSS is applied by measuring a concomitant variable is proposed by Zamanzade and Vock [22]. Their estimator was obtained by conditioning on observed concomitant values and using nonparametric kernel regression.…”

Distribution function estimation using concomitant-based ranked set sampling

“…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. As the ranking process in RSS is performed without obtaining precise values of the sample units, it may not to be accurate (perfect).…”

“…Frey [3] and Li and Balakrishnan [5] proposed some nonparametric tests for assessing perfect ranking assumption which were followed by Vock and Balakrishnan [13], Zamanzade et al [14] and Zamanzade et al [15]. The problem of estimating the population mean and variance when RSS is applied by measuring a concomitant variable were discussed by Frey [4], Zamanzade and Mohammadi [17] and Zamanzade and Vock [16]. In this work, we plan to develop a more efficient CDF estimator when judgment ranking is performed using a concomitant variable.…”

Some nonparametric tests of perfect judgment ranking for judgment post stratification

“…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. Ratio estimator for the population mean using ranked set sampling has been addressed by Kadilar et al (2009), andLi et al (2012) analysed rounded ranked set sample data.…”