Sensitivity Analysis of a New Family of Mean-Based Estimators Under Systematic Sampling: A Computational Statistics Perspective

The availability of auxiliary information has encouraged the development of increasingly efficient estimators for population mean estimation under systematic sampling. Motivated by this, the present study introduces a new family of mean-based estimators by combining power transformations with an exponential adjustment mechanism. The proposed family offers considerable flexibility through different choices of transformation parameters, enabling it to adapt to a variety of population characteristics. Approximate expressions for the bias and mean squared error are derived using first-order approximations, and the unknown constants are determined by minimizing the mean squared error. In addition, theoretical efficiency conditions are established to compare the proposed family with several existing estimators available in the systematic sampling literature. The performance of the proposed estimators is investigated through a systematic sensitivity analysis using three generated populations and three real populations with different characteristics. The findings show that the proposed sub-classes consistently achieve lower mean squared errors and higher percent relative efficiencies than the competing estimators across the parameter combinations considered. Furthermore, the results demonstrate that increasing the value of the exponential adjustment parameter generally improves estimation efficiency, while several sub-classes maintain superior performance under different population settings. Overall, the proposed family provides a flexible and effective approach for improving population mean estimation in systematic sampling.