{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:56:09Z","timestamp":1776840969779,"version":"3.51.2"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":8046,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1987,2]]},"abstract":"<jats:p>This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of \u201ccloseness\u201d of probability density functions, it shows how<jats:italic>any<\/jats:italic>two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into \u201cglobally\u201d and \u201cpartially\u201d non-nested hypotheses. Secondly, by emphasizing the distinction between a \u201clocal null\u201d and a \u201clocal alternative,\u201d the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of \u201ccloseness\u201d of the alternative to the null hypothesis.<\/jats:p>","DOI":"10.1017\/s0266466600004138","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:48:29Z","timestamp":1236700109000},"page":"69-97","source":"Crossref","is-referenced-by-count":42,"title":["Global and Partial Non-Nested Hypotheses and Asymptotic Local Power"],"prefix":"10.1017","volume":"3","author":[{"given":"M. Hashem","family":"Pesaran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600004138_ref016","volume-title":"Information Theory and Statistics","author":"Kullback","year":"1959"},{"key":"S0266466600004138_ref015","first-page":"19","article-title":"Robust properties of likelihood ratio tests","volume":"69","author":"Kent","year":"1982","journal-title":"Biometrika"},{"key":"S0266466600004138_ref010","doi-asserted-by":"publisher","DOI":"10.2307\/2297286"},{"key":"S0266466600004138_ref006","first-page":"105","article-title":"Tests of separate families of hypotheses","volume":"1","author":"Cox","year":"1961","journal-title":"Proceedings of the 4th Berkeley Symposium"},{"key":"S0266466600004138_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(82)90065-3"},{"key":"S0266466600004138_ref003","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177705894"},{"key":"S0266466600004138_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1911522"},{"key":"S0266466600004138_ref014","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/55.2.355"},{"key":"S0266466600004138_ref019","doi-asserted-by":"publisher","DOI":"10.2307\/1911874"},{"key":"S0266466600004138_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(81)90078-6"},{"key":"S0266466600004138_ref001","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz","year":"1964"},{"key":"S0266466600004138_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(83)90014-3"},{"key":"S0266466600004138_ref004","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177698949"},{"key":"S0266466600004138_ref002","volume-title":"Proceedings of the Second International Symposium of Information Theory","author":"Akaike","year":"1973"},{"key":"S0266466600004138_ref023","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1111\/j.2517-6161.1983.tb01235.x","article-title":"Testing separate families of hypotheses: An information criterion","volume":"45","author":"Sawyer","year":"1983","journal-title":"Journal of Statistical Society"},{"key":"S0266466600004138_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(83)90121-5"},{"key":"S0266466600004138_ref011","first-page":"43","volume-title":"Evaluating the Reliability of Macroeconomic Models","author":"Deaton","year":"1982"},{"key":"S0266466600004138_ref026","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(82)90007-0"},{"key":"S0266466600004138_ref007","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1111\/j.2517-6161.1962.tb00468.x","article-title":"Further results on tests of separate families of hypotheses","volume":"24","author":"Cox","year":"1962","journal-title":"Journal of Royal Statistical Society"},{"key":"S0266466600004138_ref017","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729694"},{"key":"S0266466600004138_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/2296710"},{"key":"S0266466600004138_ref022","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/61.3.539"},{"key":"S0266466600004138_ref024","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/69.3.587"},{"key":"S0266466600004138_ref025","doi-asserted-by":"publisher","DOI":"10.2307\/1912526"},{"key":"S0266466600004138_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/1914240"},{"key":"S0266466600004138_ref020","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/71.2.245"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600004138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T05:47:14Z","timestamp":1738993634000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600004138\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,2]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1987,2]]}},"alternative-id":["S0266466600004138"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600004138","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,2]]}}}