{"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/exact-and-approximate-computation-of-the","title":"Exact and approximate computation of the scatter halfspace depth","arxiv_id":"2208.05173","date":"2022-08-10","proceeding":null,"authors":["Xiaohui Liu","Yuzi Liu","Petra Laketa","Stanislav Nagy","Yuting Chen"],"abstract":"The scatter halfspace depth (sHD) is an extension of the location halfspace (also called Tukey) depth that is applicable in the nonparametric analysis of scatter. Using sHD, it is possible to define minimax optimal robust scatter estimators for multivariate data. The problem of exact computation of sHD for data of dimension $d \\geq 2$ has, however, not been addressed in the literature. We develop an exact algorithm for the computation of sHD in any dimension $d$ and implement it efficiently using C++ for $d \\leq 5$, and in R for any dimension $d \\geq 1$. Since the exact computation of sHD is slow especially for higher dimensions, we also propose two fast approximate algorithms. All our programs are freely available in the R package scatterdepth.","url_abs":"https://arxiv.org/abs/2208.05173v1","url_pdf":"https://arxiv.org/pdf/2208.05173v1.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":"exact-and-approximate-computation-of-the","repo_url":"https://github.com/nagystanislav/scatterdepth","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}