Use of Correlation Coefficient and Quartiles of Auxiliary Variable for Improved Estimation of Population Variance

The present paper deals with the estimation of population variance using correlation coefficient and quartiles of an auxiliary variable under simple random sampling scheme. Up to the first order of the approximation, the bias and the mean square error of the proposed estimator have been obtained. The optimum value of the characterizing scalar kappa has been obtained and for this optimum value of kappa, the minimum mean square error of the proposed estimator has also been obtained up to the first order of approximation. A comparison of the proposed estimator has been made with existing estimators of population variance under simple random sampling scheme. An empirical study is also carried out to justify the theoretical findings. An improvement over existing estimators has been shown in the sense of having lesser mean square error.