Abstract / Summary
Efficient estimation of the finite population mean is a major concern in survey sampling, especially when auxiliary information is available. This study proposes a new simple random sampling without replacement population mean estimator that combines two auxiliary variables. The proposed estimator is a hybrid of ratio-type and regression-type estimators and an alternative to the usual ratio-type and regression-type estimators, which use only one auxiliary variable. The first-order behavior of the proposed estimator is studied. In particular, we provide asymptotic formulas for its bias and mean squared error. We analyze and compare it with estimators from the literature and the conventional sample mean. Under certain conditions, the proposed estimator can perform better than the other estimators presented, especially when the auxiliary variables are strongly correlated with the study variable. To test its practical performance, we conduct numerical and simulation studies with a real and an artificially generated population. The results indicate that the proposed estimator yields lower MSEs and higher PREs than the other estimators under the simulated populations and simulation conditions considered. However, the magnitude of the gain depends on population characteristics and the correlation structure. The results indicate that the dual auxiliary information approach can improve estimation accuracy if the auxiliary information is informative enough. Thus, the proposed estimator should not be regarded as universally better in all populations; it is only useful if the relationships between the study and auxiliary variables are sufficiently strong and appropriate auxiliary information is available. The suggested approach offers a desirable alternative in certain applications in agricultural, environmental, industrial, and medical research, where informative auxiliary variables are present.