{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T22:13:55Z","timestamp":1777414435384,"version":"3.51.4"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":4638,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1996,6]]},"abstract":"<jats:p>Consider a linear regression model y<jats:sub>1<\/jats:sub> = x<jats:sub>1<\/jats:sub>\u03b2 + u<jats:sub>1<\/jats:sub>, where the u<jats:sub>1<\/jats:sub>'S afe weakly dependent random variables, the x<jats:sub>1<\/jats:sub>'s are known design nonrandom variables, and \u03b2 is an unknown parameter. We define an M-estimator \u03b2<jats:sub>n<\/jats:sub> of) \u03b2 corresponding to a smooth score function. Then, the second-order Edgeworth expansion for \u03b2<jats:sub>n<\/jats:sub> is derived. Here we do not assume the normality of (u<jats:sub>1<\/jats:sub>), and (u<jats:sub>1<\/jats:sub>) includes the usual ARMA processes. Second, we give the second-order Edgeworth expansion for a transformation T(\u03b2n) of \u03b2<jats:sub>n<\/jats:sub>. Then, a sufficient condition for <jats:italic>T<\/jats:italic> to extinguish the second-order terms is given. The results are applicable to many statistical problems.<\/jats:p>","DOI":"10.1017\/s0266466600006617","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T15:41:30Z","timestamp":1236699690000},"page":"331-346","source":"Crossref","is-referenced-by-count":5,"title":["Valid Edgeworth Expansions of M-Estimators in Regression Models with Weakly Dependent Resfduals"],"prefix":"10.1017","volume":"12","author":[{"given":"Masanobu","family":"Taniguchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Madan L.","family":"Puri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600006617_ref009","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176347375"},{"key":"S0266466600006617_ref003","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176351063"},{"key":"S0266466600006617_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(90)90017-C"},{"key":"S0266466600006617_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316429"},{"key":"S0266466600006617_ref002","volume-title":"Normal Approximation and Asymptotic Expansions.","author":"Bhattacharya","year":"1976"},{"key":"S0266466600006617_ref001","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344134"},{"key":"S0266466600006617_ref013","volume-title":"Lecture Notes in Statistics","volume":"68","author":"Taniguchi","year":"1991"},{"key":"S0266466600006617_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(87)90096-0"},{"key":"S0266466600006617_ref004","volume-title":"Time Series: Data Analysis and Theory.","author":"Brillinger","year":"1975"},{"key":"S0266466600006617_ref005","doi-asserted-by":"publisher","DOI":"10.1137\/1117075"},{"key":"S0266466600006617_ref006","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF01844607","article-title":"Asymptotic expansions for sums of weakly dependent random vectors","volume":"64","author":"Cotze","year":"1983","journal-title":"Zeitschrift fur Wahrscheinlickheits Theorie und Verwandte Gebiete"},{"key":"S0266466600006617_ref008","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348784"},{"key":"S0266466600006617_ref011","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1983.10477943"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466600006617","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T21:22:23Z","timestamp":1557696143000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466600006617\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,6]]}},"alternative-id":["S0266466600006617"],"URL":"https:\/\/doi.org\/10.1017\/s0266466600006617","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6]]}}}