On double extreme rank set sample with application to regression estimator

Double Extreme Ranked Set sampling technique (DERSS) is introduced. The relative efficiency of DERSS relative to simple random sample (SRS), ranked set sample (RSS) and extreme ranked set sample (ERSS) for estimating the population mean is investigated. Also, DERSS is used to improve the efficiency of the regression estimator when the population mean of the concomitant (auxiliary) variable is unknown. We show that DERSS gives an unbiased estimator for the population mean when the underlying distribution of the variable of interest is assumed to be symmetric. Also, DERSS is more efficient than SRS, ERSS and RSS (in some cases), using the same number of quantified units. Furthermore, we show that using DERSS for estimating the population mean using regression method of estimation is more efficient than using SRS, ERSS and RSS. A simulation study is conducted to compare the efficiency of the estimators. The method is illustrated by using real data from Iowa Rural Health Study (RHS).