{"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/a-note-on-local-linear-regression-for-time","title":"A Note on Local Linear Regression for Time Series in Banach Spaces","arxiv_id":"2503.15039","date":"2025-03-19","proceeding":null,"authors":["Florian Heinrichs"],"abstract":"This work extends local linear regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates. Simulation studies assess the finite sample performance of these estimators and compare them with the Nadaraya-Watson estimator. Additionally, the proposed methods are applied to smooth EEG recordings for reconstructing eye movements and to video analysis for detecting pedestrians and abandoned objects.","url_abs":"https://arxiv.org/abs/2503.15039v1","url_pdf":"https://arxiv.org/pdf/2503.15039v1.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":"a-note-on-local-linear-regression-for-time","repo_url":"https://github.com/florianheinrichs/banach_space_llr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}