Development of efficient finite population mean estimators using transformed auxiliary variables and hierarchical clustering-based stratification

Vollständiger Abstract

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Abstract Efficient estimation of a finite population mean depends on both estimator formulation and the quality of the strata. This study develops three classes of mean estimators under stratified simple random sampling without replacement by integrating transformed auxiliary information with data-driven stratification. Auxiliary information available for all population units is first used to construct pre-sampling strata through Ward’s hierarchical clustering, thereby reducing dependence on subjective stratification. Seven transformations of the auxiliary variable are represented through common transformation factors and incorporated into optimized ratio-, product-, and exponential-type estimator structures. First-order expressions for bias and mean squared error (MSE), optimum constants, minimum MSEs, and efficiency conditions are derived. Performance is evaluated using five empirical populations and a Monte Carlo simulation covering small, medium, and large sample sizes (n = 50, 150, and 300) under low, moderate, and high correlation levels. Efficiency is measured through percentage relative efficiency (PRE), while the repeated-sampling behavior of bias and MSE across sample sizes and correlation levels is used to assess empirical stability and consistency. In the examined settings, the proposed estimators generally yield smaller MSEs and higher PREs than the competing estimators, with larger gains under stronger correlation and more homogeneous data-driven strata. These findings support the combined contribution of transformed auxiliary information and objective pre-sampling stratification, while remaining conditional on reliable frame-level auxiliary information, appropriate clustering choices, and stable estimation of the optimum constants.