Rescaling Bootstrap Variance Estimation of Level-0 Ranked Set Sampling under Finite Population Framework

Abstract

McIntyre (1952) introduced Ranked Set Sampling (RSS) to advance upon Simple Random Sampling (SRS) for circumstances where any preliminary ranking of sampled units is possible for variable of interest using visual inspection or some other means without physically measuring the units. Further, the RSS was classified into three sampling protocols named as Level-0, Level-1 and Level-2 (Deshpande et al., 2006). The Level-0 sampling protocol of RSS is considered in this article. Estimating the variance of the Level-0 RSS estimator under the finite population framework was found to be cumbersome. In this article, two distinct rescaling bootstrap with replacement methods known as Strata-based rescaling bootstrap with-replacement (SRBWR) method and Cluster-based rescaling bootstrap with-replacement (CRBWR) method have been proposed to unbiasedly estimate the variance of Level-0 RSS estimator of finite population mean. Rescaling factors are obtained for both the proposed methods to estimate the variance of the Level-0 RSS estimator unbiasedly. The results of the simulation analysis, together with real data application support, proposed methods are capable of estimating the variance of the Level-0 RSS estimator almost unbiasedly. The developed SRBWR method performs better than the CRBWR method considering Relative stability (RS) and percentage Relative Bias (%RB) for various combinations of set size (m) and several cycles (r).