Estimation of Median in Two-Phase Sampling Using Two Auxiliary Variables

A general family of estimators for estimating the population median is proposed by making use of two auxiliary variables in two-phase sampling. Under simple random sampling without replacement (SRSWOR) scheme, the expressions for bias and mean square error (MSE) of the proposed estimators are given. The minimum MSE of the proposed estimator is equal to the minimum MSE of the Singh et al. (2006 Singh , S. , Singh , H. P. , Upadhyaya , L. N. ( 2006 ). Chain ratio and regression type estimators for median estimation in survey sampling . Statist. Pap. 48 : 23 – 46 .[Crossref], [Web of Science ®] , [Google Scholar]) estimator which is more efficient than many of the existing estimators. The proposed estimator, however, has less bias as compared to the Singh et al. (2006 Singh , S. , Singh , H. P. , Upadhyaya , L. N. ( 2006 ). Chain ratio and regression type estimators for median estimation in survey sampling . Statist. Pap. 48 : 23 – 46 .[Crossref], [Web of Science ®] , [Google Scholar]) estimator. An efficiency and bias comparison is provided using three data sets.