New strategies for finite population mean estimation under non-response: Theory and application to education data

The survey sampling designs are generally affected by non-response, which causes bias and inefficiency in the estimators of population parameters. To overcome this problem, in the present study, we construct a new class of estimators for the finite population mean under a stratified random sampling scheme when there is non-response. One of the salient dimensions of our method is the explicit use of dual auxiliary information within a stratified design framework to account for population heterogeneity within strata, which has not been systematically highlighted earlier. Two types of non-response are studied: one where the missing values arise only in the study variable, and another where both the study and auxiliary variables are subject to this response process. The bias, mean squared error (MSE) and efficiency of the proposed estimators are obtained under theoretical properties at the first-order approximation. Their finite performance is also examined via a real education survey and Monte Carlo simulation studies. The results indicate that the suggested estimators have smaller MSE and higher per cent relative efficiency (PRE) than existing ones. Graphical investigations at various threshold values of k indicate the effectiveness of the proposed estimators in practice, with a slight trade-off in efficiency as k increases. In the general context, this demonstrates that assessing more than one auxiliary with stratified sampling under non-response allows us to achieve a more precise and efficient mean estimate. This makes the proposed estimators a convenient and efficient tool for large-scale surveys where complete response data is seldom available.