{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T08:05:06Z","timestamp":1770969906556,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[1998,10,1]],"date-time":"1998-10-01T00:00:00Z","timestamp":907200000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1998,10]]},"abstract":"<jats:p>Many estimators and tests are of the form of a \nratio of quadratic forms in normal variables. Excepting \na few very special cases little is known about the density \nor distribution of these ratios, particularly if we allow \nfor noncentrality in the quadratic forms. This paper assumes \nthis generality and derives saddlepoint approximations \nfor this class of statistics. We first derive and prove \nthe existence of an exact inversion based on the joint \ncharacteristic function. Then the saddlepoint algorithm \nis applied and the leading term found, and analytic justification \nof the asymptotic nature of the approximation is given. \nAs an illustration we consider the calculation of sizes \nand powers of <jats:italic>F<\/jats:italic>-tests, where a new exact result \nis found.<\/jats:p>","DOI":"10.1017\/s0266466698145012","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:45:46Z","timestamp":1027763146000},"page":"539-559","source":"Crossref","is-referenced-by-count":16,"title":["SADDLEPOINT APPROXIMATIONS FOR NONCENTRAL QUADRATIC FORMS"],"prefix":"10.1017","volume":"14","author":[{"given":"Patrick W.N.","family":"Marsh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[1998,10,1]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466698145012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T16:02:58Z","timestamp":1557504178000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466698145012\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,10]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1998,10]]}},"alternative-id":["S0266466698145012"],"URL":"https:\/\/doi.org\/10.1017\/s0266466698145012","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,10]]}}}