{"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/estimation-and-convergence-rates-in-the","title":"Estimation and convergence rates in the distributional single index model","arxiv_id":"2310.13973","date":"2023-10-21","proceeding":null,"authors":["Fadoua Balabdaoui","Alexander Henzi","Lukas Looser"],"abstract":"The distributional single index model is a semiparametric regression model in which the conditional distribution functions $P(Y \\leq y | X = x) = F_0(\\theta_0(x), y)$ of a real-valued outcome variable $Y$ depend on $d$-dimensional covariates $X$ through a univariate, parametric index function $\\theta_0(x)$, and increase stochastically as $\\theta_0(x)$ increases. We propose least squares approaches for the joint estimation of $\\theta_0$ and $F_0$ in the important case where $\\theta_0(x) = \\alpha_0^{\\top}x$ and obtain convergence rates of $n^{-1/3}$, thereby improving an existing result that gives a rate of $n^{-1/6}$. A simulation study indicates that the convergence rate for the estimation of $\\alpha_0$ might be faster. Furthermore, we illustrate our methods in a real data application that demonstrates the advantages of shape restrictions in single index models.","url_abs":"https://arxiv.org/abs/2310.13973v2","url_pdf":"https://arxiv.org/pdf/2310.13973v2.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":"estimation-and-convergence-rates-in-the","repo_url":"https://github.com/alexanderhenzi/distr_single_index","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}