A new family of estimators of the population variance using information on population variance of auxiliary variable in sample surveys

Abstract

This paper proposes a family of estimators of population variance S2y of the study variable y in the presence of known population variance S2x of the auxiliary variable x. It is identified that in addition to many, the recently proposed classes of estimators due to Sharma and Singh (2014) and Singh and Pal (2016) are members of the proposed family of estimators. Asymptotic expressions of bias and mean squared error (MSE) of the suggested family of estimators have been obtained. Asymptotic optimum estimator (AOE) in the family of estimators is identified. Some subclasses of estimators of the proposed family of estimators have been identified along with their properties. We have also given the theoretical comparisons among the estimators discussed in this paper.