Ranked Set Sampling for Small Area Estimation using Auxiliary Data: Insights from Crop Production Data - Anoop Kumar; Shashi Bhushan; Rohini Pokhrel (Journal of the Indian Society of Agricultural Statistics, 2025)
Small area estimation (SAE) is a critical statistical approach used to generate credible estimates for subpopulations or regions with small sample numbers. In agricultural research, reliable crop production estimation at small geographical scales is critical for policy development, resource allocation, and decision-making. Ranked set sampling (RSS), which is recognised for being a cost-effective and accurate data gathering method, is combined with auxiliary data to increase accuracy of the estimates for small regions. This study proposes synthetic ratio type estimators by combining RSS with auxiliary information to improve SAE efficiency and precision, notably in agricultural production estimation. The mean square error (MSE) of the proposed synthetic estimator is obtained to the first order approximation. The approach uses auxiliary information to lower the MSE of the estimators. Comparative investigations with certain well-known adapted SAE estimators reveal that using RSS and auxiliary data considerably improves estimation accuracy for small regions. The theoretical results are supported with a simulation study carried out over an artificially rendered population. The practical benefits of the suggested estimator are demonstrated by an application to crop production data. The findings indicate that this technique is not only more efficient, but also highly applicable in real-world agricultural surveys, making it a useful tool for improving small area estimates in resource-constrained contexts.