New Scheme of Empirical Likelihood Method for Ranked Set Sampling: Applications to Two One-Sample Problems

Abstract

We propose a novel empirical likelihood (EL) approach for ranked set sampling (RSS) that leverages the ranking structure and information of the RSS. Our new proposal suggests constraining the sum of the within-stratum probabilities of each rank stratum to (Formula presented.), where (Formula presented.) is the number of rank strata. The use of the additional constraints eliminates the need of subjective weight selection in unbalanced RSS and facilitates a seamless extension of the method for balanced RSS to unbalanced RSS. We apply our new proposal to testing one sample population mean and evaluate its performance through a numerical study and two real-world data sets, examining obesity from body fat data and symmetry of dental size from human tooth size data. We further consider the extension of the proposed EL method to jackknife EL.