{"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/finite-sample-rousseeuw-croux-scale","title":"Finite-sample Rousseeuw-Croux scale estimators","arxiv_id":"2209.12268","date":"2022-09-25","proceeding":null,"authors":["Andrey Akinshin"],"abstract":"The Rousseeuw-Croux $S_n$, $Q_n$ scale estimators and the median absolute deviation $\\operatorname{MAD}_n$ can be used as consistent estimators for the standard deviation under normality. All of them are highly robust: the breakdown point of all three estimators is $50\\%$. However, $S_n$ and $Q_n$ are much more efficient than\\ $\\operatorname{MAD}_n$: their asymptotic Gaussian efficiency values are $58\\%$ and $82\\%$ respectively compared to $37\\%$ for\\ $\\operatorname{MAD}_n$. Although these values look impressive, they are only asymptotic values. The actual Gaussian efficiency of $S_n$ and $Q_n$ for small sample sizes is noticeable lower than in the asymptotic case. The original work by Rousseeuw and Croux (1993) provides only rough approximations of the finite-sample bias-correction factors for $S_n$, $Q_n$ and brief notes on their finite-sample efficiency values. In this paper, we perform extensive Monte-Carlo simulations in order to obtain refined values of the finite-sample properties of the Rousseeuw-Croux scale estimators. We present accurate values of the bias-correction factors and Gaussian efficiency for small samples ($n \\leq 100$) and prediction equations for samples of larger sizes.","url_abs":"https://arxiv.org/abs/2209.12268v1","url_pdf":"https://arxiv.org/pdf/2209.12268v1.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":"finite-sample-rousseeuw-croux-scale","repo_url":"https://github.com/andreyakinshin/paper-frc","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}