Calibration Estimation of Population Total in Two-Stage Sampling Design under unavailability of Population Level Auxiliary Information for the selected PSUs

 Calibration approach is a popular technique in sample surveys which incorporates auxiliary information in the estimation process assuming that population aggregates of auxiliary variable are available. Many often under two-stage sampling design, such population aggregates of auxiliary variable, i.e., population mean or total are unavailable and under such situations, estimation of population total has been limited to the use of two phase sampling. Therefore, in the present study, efficient estimator of population total is developed under two-stage sampling design when population aggregates of auxiliary variable are unavailable for the selected psu’s. The calibrated estimator is developed using the information on known population aggregates of additional auxiliary variable which is less linearly related to the study variable through two step calibration approach. The approximate variance and variance estimator of the proposed calibrated estimator has also been developed. Empirical evaluations using both real and simulated data shows the superior performance of the developed calibrated estimator in comparison to the existing estimators.