Simulation based new method for population variance using auxiliary information

The efficiency of survey sampling procedures is strongly influenced by the accurate estimation of population variance, which supports precise decision-making in agriculture, economics, and social sciences. To cope with this, the researchers have considered using auxiliary information to increase the efficiency of estimators. This paper presents a new simulation based estimator for estimation of population variance that uses auxiliary information to enhance efficiency of the estimator. The bias and mean squared error (MSE) are determined up to the first-order approximation. To check efficiency of the suggested estimator, we compare it with adopted existing estimators using real data sets. Simulation study is performed in order to estimate the proposed estimator in relation to various sample sizes, correlation values, and population structures. The findings show that the new estimator is always superior to the conventional unbiased estimator of variance and other means of auxiliary variables in MSE and relative efficiency. The numerical findings specify that the recommended estimator perform high gains in terms of efficiency especially when the correlation among the study and auxiliary variable is strong. The proposed methodology is a valuable addition to the theory of survey sampling and a practical approach that would help the researchers and practitioners who want to have an effective method of estimating variance with precision.