A logarithmic-type estimator for finite population variance and its efficiency properties

This study proposes a novel logarithmic-type estimator for the finite population variance. We derive the mean square error (MSE) expressions, approximated to the first order, along with the associated efficiency conditions for the proposed estimator, as well as for several existing estimators from the literature. A comprehensive simulation study is conducted to compare the efficiency of the new estimator against these established methods. Based on the analysis of a real dataset, the results demonstrate that the proposed estimator achieves the minimum mean square error and satisfies all relevant efficiency criteria. Consequently, it is concluded that the proposed estimator outperforms the other considered estimators in terms of efficiency.