On the use of antithetic variables to improve over the ranked set sampling estimator of the population mean

Abstract

In the ranked set sampling algorithm a sample of size n2 is available. The data can be ranked without measurements. A subsample of size n is created using the information given by the ranks. The population mean is estimated by the subsample mean. In this paper, we investigate other ways for creating the subsample. To this end we introduce new sampling algorithms using the idea of antithetic variables. We propose a class of random estimators for the population mean which covers the ranked set sampling and simple random sampling estimators as special cases. A general dominance result leading to a suffcient condition for a random estimator \(\hat \mu _1\) to dominate another random estimator \(\hat \mu _2\) is established. The theory is done in a completely nonparametric basis and without making any assumption about the distribution of the underlying population. Finally, the superiority of our proposed estimators over the ranked set sampling estimator is established and the obtained results are evaluated through examples and numerical studies.