{"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/inverse-set-estimation-and-inversion-of","title":"Inverse set estimation and inversion of simultaneous confidence intervals","arxiv_id":"2210.03933","date":"2022-10-08","proceeding":null,"authors":["Junting Ren","Fabian J. E. Telschow","Armin Schwartzman"],"abstract":"Motivated by the questions of risk assessment in climatology (temperature change in North America) and medicine (impact of statin usage and COVID-19 on hospitalized patients), we address the problem of estimating the set in the domain of a function whose image equals a predefined subset. Existing methods that construct confidence sets require strict assumptions. We generalize the estimation of such sets to dense and non-dense domains with protection against \"data peeking\" by proving that confidence sets of multiple levels can be simultaneously constructed with the desired confidence non-asymptotically through inverting simultaneous confidence bands. A non-parametric bootstrap algorithm and code are provided.","url_abs":"https://arxiv.org/abs/2210.03933v3","url_pdf":"https://arxiv.org/pdf/2210.03933v3.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":"inverse-set-estimation-and-inversion-of","repo_url":"https://github.com/junting-ren/inverse_set_sci","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}