Estimation using two-sample and large sample theory in ranked set sampling

A large-sample test for testing the equality of two population means based on ranked set samples (RSS) is presented. The null and alternative distributions of the proposed test statistic are derived. The main theme here is to produce natural adaptive estimators with some desirable statistical properties. In the context of two arbitrary models, the expressions for the asymptotic mean squared error of the proposed estimators are presented and compared with the parallel expressions for the classical estimators. We demonstrate that the suggested preliminary test estimator has superior asymptotic mean squared error performance relative to the classical and pooled estimators. A simulation study and application of the methodology to real data are showcased.