Ratio estimators of the population mean with missing values using ranked set sampling

Abstract

The existence of missing observations (MO) is commonly solved by using imputation methods. There are ratio‐based methods for estimating the population mean, while using simple random sampling (SRS), when MO are present. Considering the existence of MO and using of ranked set sampling, we develop a study of the estimation of a population mean using ratio‐based methods. The mean square errors, bias, and gain in accuracy formulas of the suggested estimators are derived. The suggested estimators are compared with their SRS counterpart both theoretically and numerically. Copyright © 2014 John Wiley & Sons, Ltd.

New ranked set sampling for estimating the population mean and variance

“…For k = 6, we have to select 36 units from the population and then measure only 6 units of them to be a neoteric ranked set sample which are Y [4] , Y [9] , Y [16] , Y [21] , Y [28] , Y [33] .The NRSS mean estimator can be obtained as…”

“…[4] , Y [9] ) + Cov ( Y [4] , Y [16] ) + Cov ( Y [4] , Y [21] ) + Cov ( Y [4] , Y [28] ) + Cov ( Y [4] , Y [33] ) + Cov ( Y [9] , Y [16] ) + Cov ( Y [9] , Y [21] ) + Cov ( Y [9] , Y [28] ) + Cov ( Y [9] , Y [33] ) + Cov ( Y [16] , Y [21] ) …”

“…Bouza [7] and Al-Omari and Bouza [4] considered the problem of estimation of population mean in the RSS with missing values. Al-Saleh and Al-Omari [5], Al-Omari and Al-Saleh [3] and Al-Omari [1], [2] proposed some mean estimators in other variations of the RSS.…”

Simulation studies to examine bias and precision of some estimators that use auxiliary information in design-based sampling in forest inventory

“…These are used in many areas of research, including economics (Knottnerus 2011), medicine (Al-Omari andBouza 2015), agriculture (Francis et al 1979;Reich et al 1993), land-use assessment (Li et al 2014) and animal ecology (Stevenson 1979;Neilson et al 2013). Their principles are described by Cochran (1977, Chap.…”

“…6) and theoreticians continue to develop them for particular circumstances (e.g. Oral and Oral 2011;Lin and Chao 2014;Magnussen et al 2014;Al-Omari and Bouza 2015;Weiskittel et al 2015;Kumar and Chhaparwal1 2016;Ringvall et al 2016). Another method that is being used increasingly is 'model-assisted' estimation; Baffetta et al (2009) offer a formal and generalised description of its approach whilst Kangas et al (2016) offer a recent example of its use.…”