Geometric Fusion Mechanism for Reliable Central Measure Construction Amid Partial and Distorted Information

Biased estimates and fluctuating measures of central tendency are significant impediments to statistical inference and computational data analysis and are often caused by partial and distorted observations. The imputed least-squares-based estimators are very sensitive to non-normality, outliers, and missing data; thus, they cannot guarantee reliability in the presence of anomalous data. In an attempt to overcome these inadequacies, this paper utilizes a geometric fusion scheme, the Minimum Regularized Covariance Determinant (MRCD), to construct high-quality central measures. The suggested mechanism incorporates the concept of geometric dispersion and resistance-based principles of covariance to form stable dispersion structures, irrespective of data contamination and incompleteness. In this computational scheme, three estimators are developed, all of which use adaptive logarithmic transformations to boost efficiency and robustness. The theoretical argument can be characterized by analytical derivations of bias and Mean Squared Error (MSE) in large-sample situations, and empirical gains were verified by large-scale Monte Carlo experiments using synthetic populations and real-world datasets. The proposed MRCDdriven estimators are known to have a lower MSE as well as higher percentage relative efficiency (PRE) as compared to classical estimators. Overall, the findings indicate that the geometric fusion mechanism (MRCD) is a powerful, self-scaling, and statistically sound way of computing central measures in a situation in which information is incomplete and distorted.