{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T01:29:55Z","timestamp":1790386195986,"version":"4.1.0"},"reference-count":61,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2019,6,9]],"date-time":"2019-06-09T00:00:00Z","timestamp":1560038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100008982","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008982","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,9,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein\u2013von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial-based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of confidence intervals for competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.<\/jats:p>","DOI":"10.1093\/biomet\/asz016","type":"journal-article","created":{"date-parts":[[2019,3,10]],"date-time":"2019-03-10T20:06:51Z","timestamp":1552248411000},"page":"501-518","source":"Crossref","is-referenced-by-count":31,"title":["Nonparametric generalized fiducial inference for survival functions under censoring"],"prefix":"10.1093","volume":"106","author":[{"given":"Y","family":"Cui","sequence":"first","affiliation":[{"name":"Department of Statistics, The Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, Pennsylvania 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J","family":"Hannig","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, 318 Hanes Hall, Chapel Hill, North Carolina 27599, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,6,9]]},"reference":[{"key":"2019091012205861100_B1","first-page":"1032","article-title":"Bootstrapping the Kaplan-Meier estimator","volume":"81","author":"Akritas,","year":"1986","journal-title":"J. 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