On Model Improvement Algorithms—Generalised Linear Models and Neural Networks

We propose a generic approach to stochastic model improvement by first introducing an archetypal algorithm based on error minimisation and establishing two results on the weak convergence of the probability laws associated with the models under improvement. We then present two concrete instances of this approach: Generalised Linear Models and classical multivariate models assessed using a neural network. In both cases, we illustrate the methodology using economic, financial, and social data related to the determination of government bond coupon rates prior to primary market auctions. For each application, we derive weak convergence results that specify conditions under which model improvement occurs, in the sense of convergence in law of the probability distributions associated with successive models. These results ensure the convergence of the proposed archetypal algorithm and provide a probabilistic foundation for systematic model improvement.