{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T06:09:40Z","timestamp":1770876580736,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T00:00:00Z","timestamp":1770163200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT","award":["UID\/297\/2025"],"award-info":[{"award-number":["UID\/297\/2025"]}]},{"name":"FCT","award":["UID\/PRR\/297\/2025"],"award-info":[{"award-number":["UID\/PRR\/297\/2025"]}]},{"name":"FCT","award":["UID\/06522\/2025"],"award-info":[{"award-number":["UID\/06522\/2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/math14030561","type":"journal-article","created":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T13:56:23Z","timestamp":1770213383000},"page":"561","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Model Improvement Algorithms\u2014Generalised Linear Models and Neural Networks"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4991-7568","authenticated-orcid":false,"given":"Manuel L.","family":"Esqu\u00edvel","sequence":"first","affiliation":[{"name":"Department of Mathematics, NOVA School of Science and Technology (NOVA FCT), 2829-516 Caparica, Portugal"},{"name":"Center for Mathematics and Applications (NOVA Math), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4226-1658","authenticated-orcid":false,"given":"Nadezhda P.","family":"Krasii","sequence":"additional","affiliation":[{"name":"Center for Mathematics and Applications (NOVA Math), Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"},{"name":"Department of Higher Mathematics, Don State Technical University, Gagarin Square 1, Rostov-on-Don 344000, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3294-3962","authenticated-orcid":false,"given":"Raquel M.","family":"Gaspar","sequence":"additional","affiliation":[{"name":"ISEG Research, Lisbon School of Economics and Management, Universidade de Lisboa, 1200-781 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,4]]},"reference":[{"key":"ref_1","unstructured":"Marketing and Communication Department (2014). 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