{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T12:25:44Z","timestamp":1791894344447,"version":"4.3.4"},"reference-count":13,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1960,1,1]],"date-time":"1960-01-01T00:00:00Z","timestamp":-315619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1960,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>The statistical properties of the approximate confidence regions for nonlinear estimation based on the likelihood ratio criterion are considered, assuming normal variation of errors. It is suggested that these approximate confidence regions are preferable to any known exact confidence regions for this problem, provided that the model is only moderately non-linear.<\/jats:p>\n                  <jats:p>A numerical measure of the non-linearity of a model (as a function of the experimental design and the parameter values) is proposed. This can be used to indicate: (a)the accuracy of these approximate confidence regions, and a simple method of modifying the regions to avoid exaggerating the significance of the experimental data in doubtful cases; and(b)the effectiveness of a non-linear transformation of parameters as a device for making the model approximately linear.<\/jats:p>\n                  <jats:p>Methods of computing the non-linearity so defined, either empirically or theoretically, are indicated.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1960.tb00353.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T01:35:59Z","timestamp":1544146559000},"page":"41-76","source":"Crossref","is-referenced-by-count":386,"title":["Confidence Regions in Non-Linear Estimation"],"prefix":"10.1093","volume":"22","author":[{"given":"E. M. L.","family":"Beale","sequence":"first","affiliation":[{"name":"Admiralty Research Laboratory , Teddington"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090921022680100_cit1","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1093\/biomet\/40.1-2.12","article-title":"Approximate confidence intervals","volume":"40","author":"Bartlett","year":"1953","journal-title":"Biometrika"},{"key":"2024090921022680100_cit2","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1093\/biomet\/40.1-2.12","article-title":"Approximate confidence intervals II. More than one unknown parameter","volume":"40","author":"Bartlett","year":"1953","journal-title":"Biometrika"},{"key":"2024090921022680100_cit3","first-page":"201","article-title":"Approximate confidence intervals III. A bias correction","volume":"42","author":"Bartlett","year":"1955","journal-title":"Biometrika"},{"key":"2024090921022680100_cit4","first-page":"251","article-title":"Contribution to the discussion of F. Yates, M. J. R. Healy and S. Lipton\u2019s paper \u2018Routine analysis of replicated experiments on an electronic computer","volume":"19","author":"Box","year":"1957","journal-title":"J. R. Statist. Soc., B"},{"issue":"B","key":"2024090921022680100_cit5","first-page":"100","article-title":"Application of digital computers in the exploration of functional relationships","volume":"103","author":"Box","year":"1956","journal-title":"Proc. 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Statist."},{"key":"2024090921022680100_cit12","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1214\/aoms\/1177732181","article-title":"An optimum property of confidence regions associated with the likelihood function","volume":"10","author":"Wilks","year":"1939","journal-title":"Ann. Math. Statist."},{"key":"2024090921022680100_cit13","doi-asserted-by":"crossref","first-page":"285","DOI":"10.2307\/20022953","article-title":"Least squares and laws of population growth","volume":"68","author":"Wilson","year":"1933","journal-title":"Proc. Amer. Acad. Arts & Sci."}],"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.2517-6161.1960.tb00353.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/22\/1\/41\/49099078\/jrsssb_22_1_41.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/22\/1\/41\/49099078\/jrsssb_22_1_41.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T17:59:35Z","timestamp":1725904775000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/22\/1\/41\/7027982"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1960,1,1]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1960,1,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1960.tb00353.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1960,1]]},"published":{"date-parts":[[1960,1,1]]}}}