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Fisher introduced the fiducial distribution as a potential replacement for the Bayesian posterior distribution in the 1930s. During the past century, fiducial approaches have been explored in various parametric and nonparametric settings. However, to the best of our knowledge, no fiducial inference has been developed in the realm of semiparametric statistics. In this paper, we propose a novel fiducial approach for semiparametric models. In memory of Sir David Cox, who passed away in 2022, we use the Cox proportional hazards model, which is the most popular model for the analysis of survival data, as a running example. Other models and extensions are also discussed. In our experiments, we find that our method performs particularly well in situations where the maximum likelihood estimator fails.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag111","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T12:25:53Z","timestamp":1781612753000},"source":"Crossref","is-referenced-by-count":0,"title":["Semiparametric fiducial inference for Cox models"],"prefix":"10.1093","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9957-7955","authenticated-orcid":false,"given":"Yifan","family":"Cui","sequence":"first","affiliation":[{"name":"Center for Data Science, Zhejiang University , Hangzhou ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4164-0173","authenticated-orcid":false,"given":"Jan","family":"Hannig","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, University of North Carolina at Chapel Hill , Chapel Hill, NC ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Edlefsen","sequence":"additional","affiliation":[{"name":"Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center , Seattle, WA ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,7,1]]},"reference":[{"key":"2026070112134931300_qkag111-B1","first-page":"1","volume-title":"A model for nonparametric regression analysis of counting processes","author":"Aalen","year":"1980"},{"issue":"4","key":"2026070112134931300_qkag111-B2","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1214\/aos\/1176345976","article-title":"Cox\u2019s regression model for counting processes: A large sample study","volume":"10","author":"Andersen","year":"1982","journal-title":"The Annals of Statistics"},{"key":"2026070112134931300_qkag111-B3","first-page":"395","article-title":"The generalised Fisher-Behrens problem and some general principles of statistical inference","volume":"55","author":"Barnard","year":"1993","journal-title":"Sankhy\u0101: The Indian Journal of Statistics. 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