Regression-Type Imputation Scheme under Two-Stage with Unequal Chance of Random Non-Response at First Stage

This research focuses on the estimation of population mean in two-stage cluster sampling, where the firs-stage cluster units face unequal probabilities of random non-response. To address this, regression-type imputation schemes and estimators are developed, incorporating measurement error parameters for both the study and auxiliary variables. Analytical derivations and simulations demonstrate the efficiency of the proposed estimators. As shown in table 1, the proposed estimators which utilized the second auxiliary variable parameter outperform the usual mean per unit estimator and the Maji et al. (2018) estimator in Case A, both with and without measurement error. Similarly, in table 2, it can be observed that the suggested estimator ( ), is more efficient, that the usual mean per unit estimator without auxiliary information and the Maji et al. (2018) estimator, while Maji et al. (2018) estimator performed better than other estimators in the same scenario when measurement error is absence for all non-response probability selections. In another scenario, when measurement is presence, the proposed estimators are more efficient for all non-response probabilities. These results confirm the practicality and robustness of the proposed methods for estimating finite population means in the presence of non-response and measurement error.