A New Shrinkage Estimator: Theoretical Foundation and Intelligent Web Interface

This study introduces the ERSE, a novel penalization framework that enhances parameter estimation in linear mixed models through entropy-based regularization. The approach integrates a Shannon entropy term into a ridge-penalized loss function to promote coefficient shrinkage and structured dispersion. By limiting dominance from a few large coefficients, the entropy component improves estimation stability, particularly under small-sample and high-dimensional conditions. The theoretical development establishes the convexity and differentiability of ERSE and derives a closed-form gradient optimized via the L-BFGS-B algorithm. To enhance practical usability, an Intelligent Web Interface is implemented in R Shiny, embedding an adaptive agent module that interprets simulation outcomes in real time and recommends optimal tuning parameters ( λ , α ). This interface enables users to perform virtual experiments before analyzing real-world data, saving time, reducing cost, and guiding decision-making without advanced statistical expertise. Extensive simulations demonstrate that ERSE consistently outperforms benchmark estimators including GLS, Ridge, Lasso, and Elastic Net across various noise levels and sample sizes. The estimator achieves lower mean squared error and bias while maintaining stable entropy values, offering a computationally efficient and interpretable solution for modern regularized estimation and applied statistical modeling.