Calibration estimator of population mean in stratified random sampling

Stratified Sampling is one of the most widely used sampling techniques as it increases the precision of the estimate of the survey variable. On the other hand, calibration estimation is a method of adjusting the original design weights to improve survey estimates by using auxiliary information such as the known population total (or mean) of the auxiliary variables. A calibration estimator uses calibrated weights that are determined to minimize a given distance measure to the original design weights while satisfying a set of constraints related to the auxiliary information. In this paper, a new calibration estimator of population mean in stratified sampling design is proposed, which incorporates not only the population mean but also the variance stratified mean available for the auxiliary variable. The problem of determining the optimum calibrated weights is formulated as a Nonlinear Programming Problem (NLPP) that is solved using Lagrange multiplier technique. The computational details of the procedure are illustrated in the presence of one auxiliary variable. A numerical example is presented and a simulation study is carried out to illustrate the computational details and the performance of the proposed calibration estimator. The results reveal that the proposed calibration estimator is more efficient than the other calibration estimators of the population mean.