{"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/robust-and-semiparametric-efficient","title":"Robust Semiparametric Efficient Estimators in Elliptical Distributions","arxiv_id":"2002.02239","date":"2020-02-06","proceeding":null,"authors":["Stefano Fortunati","Alexandre Renaux","Frédéric Pascal"],"abstract":"Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the \\textit{semiparametric} covariance/scatter matrix estimation problem in elliptical distributions. The class of elliptical distributions can be seen as a semiparametric model where the finite-dimensional vector of interest is given by the location vector and by the (vectorized) covariance/scatter matrix, while the density generator represents an infinite-dimensional nuisance function. The main aim of this work is then to provide possible estimators of the finite-dimensional parameter vector able to reconcile the two dichotomic concepts of \\textit{robustness} and (semiparametric) \\textit{efficiency}. An $R$-estimator satisfying these requirements has been recently proposed by Hallin, Oja and Paindaveine for real-valued elliptical data by exploiting the Le Cam's theory of \\textit{one-step efficient estimators} and the \\textit{rank-based statistics}. In this paper, we firstly recall the building blocks underlying the derivation of such real-valued $R$-estimator, then its extension to complex-valued data is proposed. Moreover, through numerical simulations, its estimation performance and robustness to outliers are investigated in a finite-sample regime.","url_abs":"https://arxiv.org/abs/2002.02239v3","url_pdf":"https://arxiv.org/pdf/2002.02239v3.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":"abstracts"},"code_links":[{"paper_slug":"robust-and-semiparametric-efficient","repo_url":"https://github.com/StefanoFor/Robust-semiparametric-efficient-R-estimator-for-shape-matrices","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"robust-and-semiparametric-efficient","repo_url":"https://github.com/StefanoFor/Computationally_efficient_version_of_the_R_estimator","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"robust-and-semiparametric-efficient","repo_url":"https://github.com/StefanoFor/Python_Robust-semiparametric-efficient-R-estimator-for-shape-matrices","is_official":0,"mentioned_in_paper":0,"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}