Calibration estimator in two stage sampling using double sampling approach when study variable is inversely related to auxiliary variable

Abstract

The calibration approach is a popular technique for incorporating auxiliary information for estimation of population parameters in survey sampling. In general, the Calibration Approach assumes the availability of population-level auxiliary information. On the contrary, in large scale surveys, it is often the case that population-level data on auxiliary variable is not available, but it is relatively inexpensive to collect. In the present article, in case of non-availability of population-level relatively inexpensive data on auxiliary variable under two stage sampling, we developed product type calibration estimator of the finite population total using double sampling approach along with the sampling variance and variance estimator. The study variable is assumed to be inversely related with the auxiliary variable. Proposed product type calibration estimator was evaluated through a simulation study which showed that the proposed product type calibration estimator was performing efficiently over traditional Narain-Horvitz-Thompson type expansion estimator as well as product estimator of the finite population total in case of two stage sampling involving two phases at both the stages.