{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/dynamic-function-on-scalars-regression","title":"Dynamic Function-on-Scalars Regression","arxiv_id":"1806.01460","date":"2018-06-05","proceeding":null,"authors":["Daniel R. Kowal"],"abstract":"We develop a modeling framework for dynamic function-on-scalars regression, in which a time series of functional data is regressed on a time series of scalar predictors. The regression coefficient function for each predictor is allowed to be dynamic, which is essential for applications where the association between predictors and a (functional) response is time-varying. For greater modeling flexibility, we design a nonparametric reduced-rank functional data model with an unknown functional basis expansion, which is data-adaptive and, unlike most existing methods, modeled as unknown for appropriate uncertainty quantification. Within a Bayesian framework, we introduce shrinkage priors that simultaneously (i) regularize time-varying regression coefficient functions to be locally static, (ii) effectively remove unimportant predictor variables from the model, and (iii) reduce sensitivity to the dimension of the functional basis. A simulation analysis confirms the importance of these shrinkage priors, with notable improvements over existing alternatives. We develop a novel projection-based Gibbs sampling algorithm, which offers unrivaled computational scalability for fully Bayesian functional regression. We apply the proposed methodology (i) to analyze the time-varying impact of macroeconomic variables on the U.S. yield curve and (ii) to characterize the effects of socioeconomic and demographic predictors on age-specific fertility rates in South and Southeast Asia.","url_abs":"http://arxiv.org/abs/1806.01460v2","url_pdf":"http://arxiv.org/pdf/1806.01460v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"dynamic-function-on-scalars-regression","repo_url":"https://github.com/drkowal/dfosr","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}