Estimation techniques utilizing dual auxiliary variables in stratified two-phase sampling

In this research paper, an improved set of estimators for finding the finite population variance of a study variable under a stratified two-phase sampling design is introduced. These estimators rely on information about extreme values and the ranks of an auxiliary variable. We examined the properties of these estimators using first-order approximation, focusing on biases and mean squared errors (MSEs). Additionally, we conducted an extensive simulation study to evaluate their performance and validate our theoretical insights. Furthermore, in the application section, we employed some datasets to further assess the performances of our estimators as compared to other existing estimators. The results demonstrated that $S_{Q_2}^2$ was the best-performing estimator, and significantly outperforms existing estimators, achieving a percent relative efficiency $(PRE)$ in the exponential distribution as high as 385.467. The percent relative efficiency values were continuously higher than 100 in a variety of situations, with values as high as 353.129 in other distributions like the uniform and gamma. The suggested estimators are superior to the conventional estimators, as demonstrated by empirical assessments using datasets, where percent relative efficiency improvements ranged from 115.026 to 139.897. These results highlight the robustness and applicability of the proposed class of estimators in real-world sampling.