{"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/on-the-choice-of-the-two-tuning-parameters","title":"On the choice of the two tuning parameters for nonparametric estimation of an elliptical distribution generator","arxiv_id":"2408.17087","date":"2024-08-30","proceeding":null,"authors":["Victor Ryan","Alexis Derumigny"],"abstract":"Elliptical distributions are a simple and flexible class of distributions that depend on a one-dimensional function, called the density generator. In this article, we study the non-parametric estimator of this generator that was introduced by Liebscher (2005). This estimator depends on two tuning parameters: a bandwidth $h$ -- as usual in kernel smoothing -- and an additional parameter $a$ that control the behavior near the center of the distribution. We give an explicit expression for the asymptotic MSE at a point $x$, and derive explicit expressions for the optimal tuning parameters $h$ and $a$. Estimation of the derivatives of the generator is also discussed. A simulation study shows the performance of the new methods.","url_abs":"https://arxiv.org/abs/2408.17087v2","url_pdf":"https://arxiv.org/pdf/2408.17087v2.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":"on-the-choice-of-the-two-tuning-parameters","repo_url":"https://github.com/AlexisDerumigny/ElliptCopulas","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}