Generalized Variance Estimator using Two Auxiliary Variables under Stratified Random Sampling

Abstract

Efficient and precise estimation in sample surveys often benefits from the incorporation of auxiliary information. This study addresses the challenge of improving variance estimation by developing a novel estimator for finite population variance that utilizes two auxiliary variables within the framework of stratified random sampling. The estimator's properties were derived using the approach of near-unbiasedness, ensuring theoretical rigor and robustness. Efficiency conditions that demonstrate the superiority of the suggested estimator over existing population variance estimators were established analytically. The performance of the proposed estimator was validated using four real datasets. From Dataset III, the estimator showed minimum bias (-6.937e-21), a mean square error of 7.991911, and a relative efficiency of 100.01%. Similarly, for Dataset IV, the proposed estimator achieved a bias of 9.249550e-22, a mean square error of 8.154949e-11, and a relative efficiency of 654.15%. In all cases, the proposed estimator outperformed the existing estimators based on the criteria of bias, mean square error, and percentage relative efficiency. These findings highlight the estimator's practical utility in delivering more accurate and reliable variance estimates across different applications. Consequently, the suggested estimator offers a significant contribution to the field, with potential for wide-ranging use in improving the quality of survey-based studies.