Estimation of finite population mean in a complex survey sampling

Accurate estimation of the finite population mean is a fundamental challenge in survey sampling, especially when dealing with large or complex populations. Traditional methods like simple random sampling may not always provide reliable or efficient estimates in such cases. Motivated by this, the current study explores complex sampling techniques to improve the precision and accuracy of mean estimators. Specifically, we employ two-stage and three-stage cluster sampling methods to develop unbiased estimators for the finite population mean. Building upon these, the next phase of the study formulates unbiased mean estimators using stratified two- and three-stage cluster sampling. To further enhance the precision of these estimators, a ranked-set sampling strategy is applied to the secondary and tertiary sampling stages. Additionally, unbiased variance estimators corresponding to the proposed mean estimators are derived. Real-world datasets are utilized to demonstrate the application of these complex survey sampling methodologies, with results showing that the mean estimates derived using ranked set sampling are more accurate than those obtained via simple random sampling.