{"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/asymptotics-of-the-discrete-log-concave","title":"Asymptotics of the discrete log-concave maximum likelihood estimator and related applications","arxiv_id":"1107.3904","date":"2011-07-20","proceeding":null,"authors":["Fadoua Balabdaoui","Hanna Jankowski","Kaspar Rufibach","Marios Pavlides"],"abstract":"The assumption of log-concavity is a flexible and appealing nonparametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator (MLE) of a probability mass function (pmf). We show that the MLE is strongly consistent and derive its pointwise asymptotic theory under both the well- and misspecified setting. Our asymptotic results are used to calculate confidence intervals for the true log-concave pmf. Both the MLE and the associated confidence intervals may be easily computed using the R package logcondiscr. We illustrate our theoretical results using recent data from the H1N1 pandemic in Ontario, Canada.","url_abs":"https://arxiv.org/abs/1107.3904v4","url_pdf":"https://arxiv.org/pdf/1107.3904v4.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":"asymptotics-of-the-discrete-log-concave","repo_url":"https://cran.r-project.org/package=logcondiscr","is_official":1,"mentioned_in_paper":0,"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}