Developing Robust Exponential Ratio and Product Estimators for Post-Stratification: Addressing Non-Response and Enhancing Accuracy Through Double Sampling

A key survey sampling technique, post stratification, involves dividing a population that is diverse into strata with rather homogeneous members in order to improve population estimates. Modern large scale surveys often suffer from non-response, and these too will yield biased results. According to this paper, a new estimator which combines non response adjustment and double sampling techniques to improve the accuracy of product type and exponential ratio estimators is introduced. The proposed estimator has lower bias and mean squared error (MSE) on population mean estimators when response rates are incomplete. Theoretical derivations and empirical analysis on two real-world datasets—one on classroom activities and the other on agricultural yields—are shown to validate the estimator's performance. The Non Response Double Sampling (NRDS) estimator turns out to be much more efficient than traditional post stratification, separate ratio, and product type exponential estimators. These results indicate that the NRDS estimator is a robust and reliable way to handle missing within units within strata in stratified surveys, and that this estimator is a better way to improve the population mean estimates under conditions of non response.