Direct and synthetic logarithmic estimators in small area estimation via ranked set sampling

This paper delves into the integration of logarithmic estimators of population mean within the framework of small area estimation (SAE) employing ranked set sampling (RSS). The properties like bias and mean square error (MSE) of the proposed estimators are studied up to first order approximation. The MSE of the proposed logarithmic estimators is compared with its rivals and the efficiency conditions are established. Through a combination of simulation studies and real-world applications utilizing crop production data, we explore the effectiveness of logarithmic estimators in enhancing precision and accuracy within SAE contexts. The simulation and real data results show that the proposed estimators dominate the existing estimators. By bridging theory with practical application, we aim to provide a comprehensive understanding of the capabilities and limitations of logarithmic estimators in this specialized area.