{"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/maximum-likelihood-estimation-of-a-likelihood","title":"Estimation of a Likelihood Ratio Ordered Family of Distributions","arxiv_id":"2007.11521","date":"2020-07-22","proceeding":null,"authors":["Alexandre Mösching","Lutz Duembgen"],"abstract":"Consider bivariate observations $(X_1,Y_1), \\ldots, (X_n,Y_n) \\in \\mathbb{R}\\times \\mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption that $Q_x$ is isotonic in $x$ with respect to likelihood ratio order. If the observations are identically distributed, a related goal is to estimate the joint distribution $\\mathcal{L}(X,Y)$ under the sole assumption that it is totally positive of order two in a certain sense. An algorithm is developed which estimates the unknown family of distributions $(Q_x)_x$ via empirical likelihood. The benefit of the stronger regularization imposed by likelihood ratio order over the usual stochastic order is evaluated in terms of estimation and predictive performances on simulated as well as real data.","url_abs":"https://arxiv.org/abs/2007.11521v4","url_pdf":"https://arxiv.org/pdf/2007.11521v4.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":"maximum-likelihood-estimation-of-a-likelihood","repo_url":"https://github.com/alexandremoesching/lrdistreg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}