{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T05:40:42Z","timestamp":1777614042126,"version":"3.51.4"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5734,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1993,6]]},"abstract":"<jats:p>Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.<\/jats:p>","DOI":"10.1017\/s0266466600007751","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:46:55Z","timestamp":1236700015000},"page":"431-450","source":"Crossref","is-referenced-by-count":20,"title":["The VPRT: A Sequential Testing Procedure Dominating the SPRT"],"prefix":"10.1017","volume":"9","author":[{"given":"Noel","family":"Cressie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter B.","family":"Morgan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600007751_ref003","doi-asserted-by":"publisher","DOI":"10.1515\/9781400874651"},{"key":"S0266466600007751_ref015","doi-asserted-by":"publisher","DOI":"10.2307\/2526776"},{"key":"S0266466600007751_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02614105"},{"key":"S0266466600007751_ref010","volume-title":"Mathematical Statistics: A Decision Theoretic Approach","author":"Ferguson","year":"1967"},{"key":"S0266466600007751_ref024","volume-title":"Sequential Analysis","author":"Wald","year":"1947"},{"key":"S0266466600007751_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/2531909"},{"key":"S0266466600007751_ref009","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1972.10488893"},{"key":"S0266466600007751_ref020","volume-title":"Applied Statistical Decision Theory","author":"Raiffa","year":"1961"},{"key":"S0266466600007751_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/1905525"},{"key":"S0266466600007751_ref002","volume-title":"Dynamic Programming","author":"Bellman","year":"1957"},{"key":"S0266466600007751_ref005","first-page":"13","article-title":"Discount optimality of Wald SPRT for iid and certain Markov dependent sequences","volume":"22","author":"Bhat","year":"1984","journal-title":"Journal of the Indian Statistical Association"},{"key":"S0266466600007751_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1911358"},{"key":"S0266466600007751_ref011","volume-title":"Sequential Tests of Statistical Hypotheses","author":"Ghosh","year":"1970"},{"key":"S0266466600007751_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/1912754"},{"key":"S0266466600007751_ref012","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346411"},{"key":"S0266466600007751_ref014","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511664342.007"},{"key":"S0266466600007751_ref016","doi-asserted-by":"publisher","DOI":"10.2307\/1912661"},{"key":"S0266466600007751_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/0095-0696(90)90056-5"},{"key":"S0266466600007751_ref019","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/64.2.191"},{"key":"S0266466600007751_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/BF02204835"},{"key":"S0266466600007751_ref026","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1111\/j.2517-6161.1965.tb00600.x","article-title":"Some general results in sequential design (with discussion)","volume":"B 27","author":"Whittle","year":"1965","journal-title":"Journal of the Royal Statistical Society"},{"key":"S0266466600007751_ref023","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800210105"},{"key":"S0266466600007751_ref025","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177730197"},{"key":"S0266466600007751_ref017","first-page":"140","article-title":"On the problem of the most efficient tests of statistical hypotheses","volume":"A 231","author":"Neyman","year":"1933","journal-title":"Philosophical Transactions of the Royal Society"},{"key":"S0266466600007751_ref013","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346416"},{"key":"S0266466600007751_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3818-8_9"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600007751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T05:47:02Z","timestamp":1738993622000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600007751\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,6]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,6]]}},"alternative-id":["S0266466600007751"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600007751","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,6]]}}}