Composite Estimators for the Population Mean Under Ranked Set Sampling

Ranked Set Sampling (RSS) is an effective sampling technique, particularly when precise measurement of the study variable is costly or time-consuming, but ranking the units is relatively easy. Estimation of the finite population mean from RSS, with and without auxiliary information, has been widely studied, with estimators such as the RSS sample mean, ratio estimator, and regression estimators receiving considerable attention. While the RSS sample mean does not utilize auxiliary information, the ratio and regression estimators rely heavily on its quality. To address these limitations, this study proposes a shrinkage-type (composite) estimator for the finite population mean. The proposed estimator adaptively combines the RSS sample mean and the ratio estimator, leveraging auxiliary information when it is useful while maintaining robustness when it is not. We derive its statistical properties, including bias, variance, and mean squared error. Simulation studies demonstrate that the proposed estimator can outperform conventional estimators across a range of scenarios. We illustrate the method through a real data application.