Variance Estimation in Sample Surveys: Utilizing Auxiliary Variable Information

This manuscript presents a novel estimator for the assessment of population variance by integrating auxiliary information pertaining to the population median and the population standard deviation. The incorporation of this dual auxiliary information empowers researchers to estimate population variance effectively, even in the presence of skewed data distributions. Utilizing Taylor’s series expansion, the formulations for both bias and mean squared error are derived, extending to the first order of approximations. To evaluate the efficacy of the proposed estimator, a comparative analysis of the mean squared error of several classical estimators is conducted, revealing that these conventional methods exhibit inferior efficiency relative to the proposed estimator. The empirical investigation demonstrates that the recommended estimator yields a lower mean squared error and possesses significant practical relevance in the context of survey sampling.