{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,26]],"date-time":"2026-07-26T07:42:18Z","timestamp":1785051738693,"version":"3.55.0"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5186,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1994,12]]},"abstract":"<jats:p>The saddlepoint approximation as developed by Daniels [3] is an extremely accurate method for approximating probability distributions. Econometric and statistical applications of the technique to densities of statistics of interest are often hindered by the requirements of explicit knowledge of the c.g.f. and the need to obtain an analytical solution to the saddlepoint defining equation. In this paper, we show the conditions under which any approximation to the saddlepoint is justified and suggest a convenient solution. We illustrate with an approximate saddlepoint expansion of the Durbin-Watson test statistic.<\/jats:p>","DOI":"10.1017\/s0266466600008914","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:41:18Z","timestamp":1236699678000},"page":"900-916","source":"Crossref","is-referenced-by-count":13,"title":["On the Approximation of Saddlepoint Expansions in Statistics"],"prefix":"10.1017","volume":"10","author":[{"given":"Offer","family":"Lieberman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600008914_ref021","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/78.4.879"},{"key":"S0266466600008914_ref015","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/65.1.91"},{"key":"S0266466600008914_ref008","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/38.1-2.159"},{"key":"S0266466600008914_ref007","first-page":"409","article-title":"Testing for serial correlation in least squares regression, I.","volume":"37","author":"Durbin","year":"1950","journal-title":"Biometrika"},{"key":"S0266466600008914_ref004","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/67.1.59"},{"key":"S0266466600008914_ref016","first-page":"199","article-title":"Large deviation expansions in econometrics.","author":"Phillips","year":"1986","journal-title":"Advances in Econometrics 5"},{"key":"S0266466600008914_ref006","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/78.1.169"},{"key":"S0266466600008914_ref020","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1990.10474927"},{"key":"S0266466600008914_ref001","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/70.2.343"},{"key":"S0266466600008914_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1403269"},{"key":"S0266466600008914_ref002","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1111\/j.2517-6161.1979.tb01085.x","article-title":"Edgeworth and saddlepoint approximations with statistical applications (with discussion).","volume":"41","author":"Barndorff-Nielsen","year":"1979","journal-title":"Journal of the Royal Statistical Society B"},{"key":"S0266466600008914_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/1909774"},{"key":"S0266466600008914_ref019","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1111\/j.2517-6161.1982.tb01191.x","article-title":"Saddlepoint approximations for permutation tests and confidence intervals.","volume":"44","author":"Robinson","year":"1982","journal-title":"Journal of the Royal Statistical Society B"},{"key":"S0266466600008914_ref018","doi-asserted-by":"publisher","DOI":"10.1137\/0901032"},{"key":"S0266466600008914_ref009","first-page":"420","article-title":"General saddlepoint approximations with applications to L statistics.","volume":"81","author":"Easton","year":"1986","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600008914_ref012","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476825"},{"key":"S0266466600008914_ref014","volume-title":"Tensor Methods in Statistics","author":"McCullagh","year":"1987"},{"key":"S0266466600008914_ref013","doi-asserted-by":"publisher","DOI":"10.2307\/1426607"},{"key":"S0266466600008914_ref003","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728652"},{"key":"S0266466600008914_ref011","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/48.3-4.419"},{"key":"S0266466600008914_ref017","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012906"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600008914","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T05:46:20Z","timestamp":1738993580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600008914\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,12]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1994,12]]}},"alternative-id":["S0266466600008914"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600008914","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,12]]}}}