Reproducibility of mean estimators under ranked set sampling

In statistical inferences, the estimation of population parameters using information obtained from a sample is an important method. This involves choosing an appropriate sampling method to collect data. An efficient sampling method used for data collection is Ranked Set Sampling (RSS). In this study, we investigate the reproducibility of four well-known mean estimators under RSS using parametric predictive bootstrapping. These estimators are called conventional, ratio, exponential ratio, and regression estimators. Reproducibility is the ability of a statistical technique to obtain results similar to those based on the original experiment if the experiment is repeated under the same conditions. We conduct a simulation study to compare the reproducibility of mean estimators for varying sample sizes when sampling is based on perfect and imperfect rankings. We consider data on abalone in our simulations to demonstrate real-world applications. This study concludes that the regression estimator is the best reproducible estimator, while the conventional estimator is the worst in this regard.