Abstract
This study introduces statistical mirroring as an innovative approach to statistical dispersion estimation, drawing inspiration from the Kabirian-based isomorphic optinalysis model, aimed at enhancing robustness and mitigating biases in estimation methods. Beyond scale-invariant characteristics, the proposed estimators emphasize scaloc-invariant robustness, thereby addressing a critical gap in dispersion estimation. By highlighting statistical meanic mirroring, alongside other forms of proposed statistical mirroring, the study underscores the adaptability and customization potential. Through extensive Monte Carlo simulations and real-life applications, in comparison with classical estimators, the results of the performance evaluation of the proposed estimators demonstrate robustness, efficiency, and transformations-invariance. The research offers a paradigm shift in addressing longstanding challenges in dispersion estimation, offering a new category of dispersion estimation and increased resistance to outliers. Notable limitations include selecting and evaluating the proposed statistical meanic mirroring under Gaussian and Gaussian mixture model distributions. This research paper significantly contributes to statistical methodologies, offering avenues for expanding knowledge in dispersion estimation. It recommends further exploration of proposed estimators across various statistical mirroring types and encourages comparative studies to establish their effectiveness, thereby advancing statistical knowledge and tools for precise data analysis.•The proposed methodology involves preprocessing transformations, statistical mirror design, and optimization to transform a univariate set into a bivariate one, facilitating the fitting of an isomorphic optinalysis model.•Estimators rely on a foundational bijective mapping of isoreflective pairs, deducing the probability of proximity or deviation from any defined center. This contrasts with classical estimators that utilize average or median deviations from a mean or median center.