{"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/regression-in-nonstandard-spaces-with-frechet","title":"Nonparametric Regression in Nonstandard Spaces","arxiv_id":"2012.13332","date":"2020-12-24","proceeding":null,"authors":["Christof Schötz"],"abstract":"A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\\'echet regression, where the value of the regression function at each point is estimated via a Fr\\'echet mean calculated from an estimated objective function. A second approach is geodesic regression, which builds upon fitting geodesics to observations by a least squares method. These approaches are applied to transform two of the most important nonparametric regression estimators in statistics to the metric setting -- the local linear regression estimator and the orthogonal series projection estimator. The resulting procedures consist of known estimators as well as new methods. We investigate their rates of convergence in a general setting and compare their performance in a simulation study on the sphere.","url_abs":"https://arxiv.org/abs/2012.13332v2","url_pdf":"https://arxiv.org/pdf/2012.13332v2.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":"regression-in-nonstandard-spaces-with-frechet","repo_url":"https://github.com/ChristofSch/spheregr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2012.13332","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}