{"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/large-sample-properties-of-partitioning-based","title":"Large Sample Properties of Partitioning-Based Series Estimators","arxiv_id":"1804.04916","date":"2018-04-13","proceeding":null,"authors":["Matias D. Cattaneo","Max H. Farrell","Yingjie Feng"],"abstract":"We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a general characterization of their leading asymptotic bias. Second, we establish integrated mean squared error approximations for the point estimator and propose feasible tuning parameter selection. Third, we develop pointwise inference methods based on undersmoothing and robust bias correction. Fourth, employing different coupling approaches, we develop uniform distributional approximations for the undersmoothed and robust bias-corrected t-statistic processes and construct valid confidence bands. In the univariate case, our uniform distributional approximations require seemingly minimal rate restrictions and improve on approximation rates known in the literature. Finally, we apply our general results to three partitioning-based estimators: splines, wavelets, and piecewise polynomials. The supplemental appendix includes several other general and example-specific technical and methodological results. A companion R package is provided.","url_abs":"https://arxiv.org/abs/1804.04916v3","url_pdf":"https://arxiv.org/pdf/1804.04916v3.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":"large-sample-properties-of-partitioning-based","repo_url":"https://github.com/nppackages-replication/CFF_2020_AOS","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"large-sample-properties-of-partitioning-based","repo_url":"https://github.com/nppackages/binsreg","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"large-sample-properties-of-partitioning-based","repo_url":"https://github.com/nppackages/lspartition","is_official":1,"mentioned_in_paper":0,"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}