This paper offers a novel approach to formulate efficient ratio estimator of the population variance using a transformed auxiliary variable. The impact of transformation on auxiliary information has also been discussed. It is observed that incorporating a transformed auxiliary variable result in a high gain in efficiency. Theoretical properties of the newly developed estimators have been derived. The empirical and simulation studies show that the suggested estimators outperformed the existing estimators.

Machine learning plays a pivotal role in addressing real-world challenges across domains such as cybersecurity, where AI-driven methods, especially in Software-Defined Networking, enhance traffic monitoring and anomaly detection. Contemporary networks often employ models like Random Forests, Neural Networks, and Support Vector Machines to identify threats early and reinforce security. Ensemble learning further improves predictive accuracy and stability, yet many frameworks falter when confronted with noisy or contaminated data. In this study, we propose a robust ensemble framework for Extreme Learning Machines (ELMs) that integrates a family of redescending ψ-activation functions grounded in M-estimation theory. Each ψ-function yields a distinct base classifier, initialized with random weights, and the optimal hidden-node count is selected via grid search minimizing the Brier score. Rather than traditional voting, ensemble outputs are combined through a least-squares optimization, allowing precise parameter estimation and enhanced stability. We validate our method on five benchmark datasets, SatImage, Email-Spamdexing, Breast Cancer, Musk, and Iris, demonstrating consistently superior accuracy and reduced variance compared to existing ELM ensembles. Rigorous statistical testing (Kruskal–Wallis with Dunn’s post-hoc comparisons) confirms these gains. Our results show that embedding robust M-estimator–based activations within a controlled ensemble yields marked improvements in generalization, predictive precision, and resilience to data irregularities, offering a significant advancement in the design of efficient neural classifiers.

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.