GLM Solutions via Shrinkage

Generalised Linear Models are a core tool for modelling non-normal data and are routinely fitted via the Iteratively Reweighted Least Squares algorithm. While this algorithm is computationally attractive, its performance can be hindered by convergence issues, sensitivity to starting values, and substantial estimation error. This paper develops a practical enhancement of the Iteratively Reweighted Least Squares algorithm by replacing the standard least squares step with Stein-type shrinkage estimators. These estimators reduce the theoretical mean squared error by introducing a controlled bias that leads to a significant variance reduction, without requiring cross-validation or increasing computational complexity. As a result, the proposed approach provides a scalable and efficient alternative to commonly used penalised generalised linear modelling. In addition, we propose an optimisation-based strategy for selecting starting values, which improves the stability and convergence of both standard and shrinkage-based Iteratively Reweighted Least Squares implementations. The paper is not primarily methodological; instead, it focuses on the practical deployment of generalised linear modelling. Extensive numerical experiments, covering a wide range of settings relevant to practitioners, together with real-data applications, demonstrate consistent improvements in accuracy, stability, and computational efficiency over the industry standard benchmarks.