Statistical modeling for multivariate population mean estimation in stratified sampling: a public health perspective
摘要
This study proposes a new multivariate ratio-type estimator for improving the estimation of population means under stratified sampling, with particular application to child mortality and parental education data. The proposed estimator incorporates two study variables the number of children ever born and the number of deaths among children under five years of age and two auxiliary variables representing the educational levels of mothers and fathers. By effectively exploiting the relationships among the study and auxiliary variables, the proposed estimator achieves greater estimation precision. Its performance is evaluated theoretically using the Mean Squared Error (MSE) and Percentage Relative Efficiency (PRE) and is compared with several existing estimators. The theoretical results are validated through both an empirical study based on a real dataset and a simulation study using a synthetic non-normal stratified population. The findings demonstrate that the proposed estimator consistently yields lower MSE and higher PRE than the competing estimators, indicating its superior efficiency and robustness. The proposed methodology has practical applications in demographic and public health surveys, particularly in studies related to fertility, child mortality, and parental education. Overall, this work contributes to the advancement of multivariate estimation techniques in stratified sampling by providing a more efficient and reliable estimator for population mean estimation.