Improvement over variance estimation using auxiliary information in sample surveys

This paper addresses the problem of estimating the population variance S²_y of the study variable y using auxiliary information in sample surveys. We have suggested a class of estimators of the population variance S²_y of the study variable y when the population variance S²_x of the auxiliary variable x is known. Asymptotic expressions of bias and mean squared error (MSE) of the proposed class of estimators have been obtained. Asymptotic optimum estimators in the proposed class of estimators have also been identified along with its MSE formula. A comparison has been provided. We have further provided the double sampling version of the proposed class of estimators. The properties of the double sampling version have been provided under large sample approximation. In addition, we support the present study with aid of a numerical illustration.