Estimation of Population Mean Using Auxiliary Attribute Information: A Comparative Study

This study presents a comparative analysis of a weighted estimator under post-stratified sampling and traditional estimators including ratio, product, exponential-ratio, exponential-product, and regression estimators in the presence of auxiliary attribute information. Although these estimators have been individually examined in the literature, their comparative performance under simple random sampling with poststratification remains unexplored. The study derives approximate expressions for the bias and mean square error (MSE) of all considered estimators and identifies conditions under which the weighted post-stratified estimator demonstrates superior efficiency. Theoretical results confirm that using auxiliary attributes at the estimation stage allows the weighted post-stratified estimator to attain lower MSE than traditional estimators. Furthermore, the study proposes a generalized Searls-type estimator, deriving expressions for its bias, minimum MSE, and optimality conditions. General criteria are also established to evaluate and compare various Searls-type estimators. A simulation study conducted in R for both the weighted post-stratified estimator and Searls form of post-stratified estimator supports the theoretical findings. Overall, the results advocate the use of weighted estimators when auxiliary attribute information is available, highlighting their applicability in diverse fields such as health, economics, education, and agriculture.