Generalized Multivariate Mixture Ratio Estimators for the Population Mean in Multi-Phase Sampling using Multi-Auxiliary Characteristics

The integration of auxiliary information into survey sampling has continued to attract significant attention in improving the efficiency of estimators. Traditional ratio and regression estimators, though effective, often show limitations when confronted with multiple auxiliary variables and complex sampling designs. This study proposed a class of Generalized Multivariate Mixture Ratio Estimators for estimating the population mean in multi-phase sampling design with multi-auxiliary characteristics. The proposed estimators extend beyond conventional single-variable approaches by combining information from several auxiliary variables and auxiliary attributes. The theoretical properties of the estimator are derived, including the Mean Square Error expressions. Theoretical comparative analysis confirmed that the proposed estimators achieved notable gains in efficiency relative to the reviewed estimators. Simulation studies further confirmed the efficiency of the proposed estimators across varying sample sizes (asymptotically), correlation structures, and distributional conditions. Overall, the generalized multivariate mixture ratio estimators confirmed to be more efficient in population mean estimation under multi-phase sampling design.