A new statistical tool with simulation and theoretical foundation: Its illustrations using the packing design and radiation data

The correct estimation of the parameter of a finite population under simple random sampling has been a major issue in survey sampling especially in cases where the auxiliary information is accessible. Despite the fact that classical estimators like ratio, product and regression estimators use auxiliary variables to enhance efficiency, they are very sensitive to certain assumptions about structure of correlation and functional form. In most real-life survey contexts, these conditions are not met to the criteria and result in inefficient efficiency improvements. This weakness creates a methodology gap in the establishment of more adaptable and effective estimators in the capacity to successfully utilize auxiliary information across dissimilar population scenarios. A new category of estimators is suggested to fill this gap by the introduction of a model that improves the estimation of the parameter of the population by maximally using auxiliary information in the framework of simple random sampling. Bias and mean squared error (MSE) theoreticalized expressions are obtained to the first order of approximation and efficiency conditions are determined by comparing the theoretical expressions to similar existing estimators analytically. An extensive simulation analysis and practical implementation have been done to analyze performance with varied correlation patterns and sample structure. The findings illustrate that the suggested estimator ensures lower MSE and higher percentage relative efficiency over the currently existing methods especially when there is moderate to strong correlation between the study and auxiliary variables. The results are in line with the development of auxiliary information-based estimation techniques and have practical implications on applied survey research.