Developing and evaluating efficient estimators for finite population mean in two-phase sampling

The estimator development process is more efficient when additional information is used. However, occasionally, it is necessary to use information regarding unknown population parameters. In these cases, we chose two-phase sampling by substituting the population mean of the supplemental variable with the sample mean from first-phase sampling. The goal of this project was to develop effective estimators of the finite population mean in a two-phase sampling scenario with a single auxiliary variable. Under certain conditions, the recommended estimators outperform the current estimators, producing biased and Mean Square Error (MSE) expressions. Empirical and theoretical comparisons of the proposed families were conducted using real and simulated data. We found that the proposed families were more effective in the two-phase sampling situation than in all-population mean estimators.