Novel efficient estimators of finite population mean in simple random sampling

This study presents a methodological advancement in survey sampling, focusing on the development of efficient estimators for the finite population mean under Simple Random Sampling without Replacement (SRSWOR). By harnessing the predictive power of correlated auxiliary variables, we formulate two innovative classes of estimators that integrate supplementary data to improve estimation accuracy. A rigorous theoretical examination is conducted, deriving first-order bias and Mean Square Error (MSE) expressions to elucidate the estimators' properties. A comprehensive evaluation framework is employed, utilizing Percentage Relative Efficiency (PRE) to assess the performance of the proposed estimators in relation to existing methods. The findings, supported by empirical analyses given in Table 3 and Figure 1 and simulation studies shown in Table 4 and Figure 2, demonstrate the superiority of the proposed estimators (y¯_Pro1, y¯_Pro2), under specific conditions, contributing to the enhancement of survey sampling methodology.