Estimation of the finite population mean using extreme values and ranks of the auxiliary variable in two-phase sampling

This study aimed to improve the estimation of the mean of the dependent variable by incorporating the smallest and largest values and ranks of the independent variable. To achieve this, we introduce two new classes of estimators that offer enhanced accuracy compared with the existing approaches, as evaluated using the mean squared error (MSE) criterion. The key features of the proposed estimators are examined through a first-order approximation method, particularly focusing on the bias and mean squared error under two-phase sampling. In addition, their performance is assessed using simulated populations generated from six different distributions with varying parameter settings, along with three real datasets. Furthermore, the findings show that the new estimators achieve lower mean squared errors compared with existing methods.