Statistical mirroring: A robust method for statistical dispersion estimation

Area of Science:

• Statistical modeling
• Robust statistics

Background:

• Classical dispersion estimation methods often lack robustness and are susceptible to biases.
• There is a critical need for advanced estimation techniques that offer scale-invariant and scaloc-invariant robustness.

Purpose of the Study:

• To introduce statistical mirroring as an innovative approach for statistical dispersion estimation.
• To develop robust and bias-mitigating estimators inspired by the Kabirian-based isomorphic optinalysis model.
• To enhance dispersion estimation by emphasizing scaloc-invariant robustness.

Main Methods:

• The methodology involves preprocessing transformations, statistical mirror design, and optimization to convert univariate data into bivariate data.
• Fitting an isomorphic optinalysis model to the transformed data.
• Developing estimators based on bijective mapping of isoreflective pairs to determine proximity or deviation from a center.

Main Results:

• Proposed statistical mirroring estimators demonstrate robustness, efficiency, and transformations-invariance compared to classical estimators.
• The new estimators offer increased resistance to outliers.
• Monte Carlo simulations and real-life applications validated the performance of the proposed methods.

Conclusions:

• Statistical mirroring represents a paradigm shift in dispersion estimation, offering a new category of estimators.
• The study highlights the adaptability and customization potential of statistical mirroring, including statistical meanic mirroring.
• Further research is recommended to explore proposed estimators across various statistical mirroring types and distributions.