Optimized Variance Estimation in Simple Random Sampling with Auxiliary Information

Abstract

In this study, we introduce an enhanced estimator for the population variance of the primary study variable under the simple random sampling without replacement (SRSWOR) framework. This estimator leverages both the correlation coefficient between the study variable and an auxiliary variable, as well as the interquartile range of the auxiliary variable. We derive the expressions for its Bias and Mean Square Error (MSE) up to the first order of approximation. Furthermore, the efficiency of the proposed estimator is evaluated by comparing its Percentage Relative Efficiency (PRE) against several existing estimators of population variance. The theoretical analysis supported by numerical illustrations using real secondary data demonstrates that the proposed estimator consistently outperforms the other estimators considered in terms of lower Bias, reduced MSE, and higher PRE.