A new statistical framework: Theoretical concepts and implementations in the fields of sports and healthcare engineering

This manuscript presents improved families of estimators that utilize mean and rank transformations of auxiliary variables. The proposed estimators serve nonlinear data structures because their performance depends on precise CDF estimations. The proposed methods address complex data challenges through their framework, which incorporates auxiliary information within a simple random sampling (SRS) design. The performance evaluation, along with injury risk analysis and strategic game planning among athletes, benefits immensely through these estimators in sports analytics. These estimators enable healthcare professionals to deliver enhanced survival analysis, along with disease progression modeling and risk assessment, when dealing with nonlinear data structures. First-order approximation techniques confirm the statistical aspects of the newly proposed estimators. Scientific studies and theoretical examinations show that the novel estimator families deliver superior mean squared error (MSE) reduction as well as enhanced percentage relative efficiency (PRE) than conventional techniques. The validated theoretical foundation concurrently demonstrates real-world applicability of the proposed estimators. Moreover, the estimation tools also prove their worth through effective usage across different practical applications, including sports and healthcare applications.