{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T18:35:40Z","timestamp":1793644540937,"version":"4.5.1"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2006,4,4]],"date-time":"2006-04-04T00:00:00Z","timestamp":1144108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Swiss National Science Foundation, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne"},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006,6,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Discrete data, particularly count and contingency table data, are typically analysed by using methods that are accurate to first order, such as normal approximations for maximum likelihood estimators. By contrast continuous data can quite generally be analysed by using third-order procedures, with major improvements in accuracy and with intrinsic separation of information concerning parameter components. The paper extends these higher order results to discrete data, yielding a methodology that is widely applicable and accurate to second order. The extension can be described in terms of an approximating exponential model that is expressed in terms of a score variable. The development is outlined and the flexibility of the approach is illustrated by examples.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00548.x","type":"journal-article","created":{"date-parts":[[2006,4,4]],"date-time":"2006-04-04T16:38:14Z","timestamp":1144168694000},"page":"495-508","source":"Crossref","is-referenced-by-count":30,"title":["Improved Likelihood Inference for Discrete Data"],"prefix":"10.1093","volume":"68","author":[{"given":"A. C.","family":"Davison","sequence":"first","affiliation":[{"name":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne , Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D. A. S.","family":"Fraser","sequence":"additional","affiliation":[{"name":"University of Toronto , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N.","family":"Reid","sequence":"additional","affiliation":[{"name":"University of Toronto , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,4,4]]},"reference":[{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/biomet\/71.1.1","article-title":"On the existence of maximum likelihood estimates in logistic regression models","volume":"71","author":"Albert","year":"1984","journal-title":"Biometrika"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3210-5","volume-title":"Inference and Asymptotics","author":"Barndorff-Nielsen","year":"1994"},{"key":"2023040708492579000_","first-page":"3","article-title":"Recovery of ancillary information","volume":"26","author":"Basu","year":"1964","journal-title":"Sankhya A"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1093\/biomet\/59.2.435","article-title":"A negative binomial model with varying element sizes","volume":"59","author":"Bissell","year":"1972","journal-title":"Biometrika"},{"key":"2023040708492579000_","volume-title":"Practical small-sample parametric inference","author":"Brazzale","year":"2000"},{"key":"2023040708492579000_","first-page":"3","volume-title":"Biostatistics Casebook","author":"Brown","year":"1980"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/S0378-3758(97)00085-2","article-title":"Likelihood centered asymptotic model exponential and location model versions","volume":"66","author":"Cakmak","year":"1998","journal-title":"J. Statist. Planng Inf."},{"key":"2023040708492579000_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511815850","volume-title":"Statistical Models","author":"Davison","year":"2003"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1093\/biomet\/89.4.933","article-title":"Saddlepoint approximations as smoothers","volume":"89","author":"Davison","year":"2002","journal-title":"Biometrika"},{"key":"2023040708492579000_","volume-title":"Statistical Methods and Scientific Inference","author":"Fisher","year":"1956"},{"key":"2023040708492579000_","volume-title":"Inference and Linear Models","author":"Fraser","year":"1979"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1093\/biomet\/90.2.327","article-title":"Likelihood for component parameters","volume":"90","author":"Fraser","year":"2003","journal-title":"Biometrika"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1214\/088342304000000323","article-title":"Ancillaries and conditional inference (with discussion)","volume":"19","author":"Fraser","year":"2004","journal-title":"Statist. Sci."},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/978-1-4613-0141-7_12","volume-title":"Empirical Bayes and Likelihood Inference","author":"Fraser","year":"2001"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1093\/biomet\/86.2.249","article-title":"A simple general formula for tail probabilities for frequentist and Bayesian inference","volume":"86","author":"Fraser","year":"1999","journal-title":"Biometrika"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"665","DOI":"10.2307\/2531094","article-title":"The analysis of rates using Poisson regression models","volume":"39","author":"Frome","year":"1983","journal-title":"Biometrics"},{"key":"2023040708492579000_","first-page":"655","article-title":"Is the \u2018improved likelihood ratio statistic\u2019 really improved in the discrete case?","volume":"76","author":"Frydenberg","year":"1989","journal-title":"Biometrika"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1093\/biomet\/86.2.265","article-title":"Improving on exact tests by approximate conditioning","volume":"86","author":"Pierce","year":"1999","journal-title":"Biometrika"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1214\/aos\/1074290325","article-title":"Asymptotics and the theory of inference","volume":"31","author":"Reid","year":"2003","journal-title":"Ann. Statist."},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1093\/biomet\/86.2.235","article-title":"An empirical adjustment to the likelihood ratio statistic","volume":"86","author":"Severini","year":"1999","journal-title":"Biometrika"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1093\/biomet\/87.4.939","article-title":"The likelihood ratio approximation to the conditional distribution of the maximum likelihood estimator in the discrete case","volume":"87","author":"Severini","year":"2000","journal-title":"Biometrika"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198506508.001.0001","volume-title":"Likelihood Methods in Statistics","author":"Severini","year":"2000"},{"key":"2023040708492579000_","doi-asserted-by":"crossref","first-page":"145","DOI":"10.2307\/3318548","article-title":"An explicit large-deviation approximation to one-parameter tests","volume":"2","author":"Skovgaard","year":"1996","journal-title":"Bernoulli"},{"key":"2023040708492579000_","first-page":"1294","article-title":"Approximately exact inference for the common odds ratio in several 2\u00d72 tables (with discussion)","volume":"93","author":"Strawderman","year":"1998","journal-title":"J. Am. Statist. Ass."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1467-9868.2006.00548.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/3\/495\/49795340\/jrsssb_68_3_495.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/3\/495\/49795340\/jrsssb_68_3_495.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T15:34:31Z","timestamp":1706974471000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/68\/3\/495\/7110654"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4,4]]},"references-count":24,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2006,4,4]]},"published-print":{"date-parts":[[2006,6,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2006.00548.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2006,6]]},"published":{"date-parts":[[2006,4,4]]}}}