{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T00:31:25Z","timestamp":1789432285940,"version":"build-2803163510"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p>This paper weakens the size and moment conditions needed for typical block bootstrap methods (i.e., the moving blocks, circular blocks, and stationary bootstraps) to be valid for the sample mean of Near-Epoch-Dependent (NED) functions of mixing processes; they are consistent under the weakest conditions that ensure the original NED process obeys a central limit theorem (CLT), established by De Jong (1997, <jats:italic>Econometric Theory<\/jats:italic> 13(3), 353\u2013367). In doing so, this paper extends De Jong\u2019s method of proof, a blocking argument, to hold with random and unequal block lengths. This paper also proves that bootstrapped partial sums satisfy a functional CLT (FCLT) under the same conditions.<\/jats:p>","DOI":"10.1017\/s0266466617000500","type":"journal-article","created":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T11:53:16Z","timestamp":1517485996000},"page":"1383-1406","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":12,"title":["BLOCK BOOTSTRAP CONSISTENCY UNDER WEAK ASSUMPTIONS"],"prefix":"10.1017","volume":"34","author":[{"given":"Gray","family":"Calhoun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2018,2,1]]},"reference":[{"key":"S0266466617000500_ref5","doi-asserted-by":"crossref","DOI":"10.1093\/0198774036.001.0001","volume-title":"Stochastic Limit Theory: An Introduction for Econometricians","author":"Davidson","year":"1994"},{"key":"S0266466617000500_ref7","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1017\/S0266466600165016","article-title":"The functional central limit theorem and weak convergence to stochastic integrals I: Weakly dependent processes","volume":"16","author":"De Jong","year":"2000","journal-title":"Econometric Theory"},{"key":"S0266466617000500_ref15","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.jkss.2011.08.009","article-title":"Bootstrap methods for dependent data: A review","volume":"40","author":"Kreiss","year":"2011a","journal-title":"Journal of the Korean Statistical Society"},{"key":"S0266466617000500_ref6","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1017\/S0266466600005843","article-title":"Central limit theorems for dependent heterogeneous random variables","volume":"13","author":"De Jong","year":"1997","journal-title":"Econometric Theory"},{"key":"S0266466617000500_ref9","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0165-1765(03)00192-7","article-title":"Consistency of the stationary bootstrap under weak moment conditions","volume":"81","author":"Gon\u00e7alves","year":"2003","journal-title":"Economics Letters"},{"key":"S0266466617000500_ref21","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1214\/aop\/1176995772","article-title":"On the invariance principle for nonstationary mixingales","volume":"5","author":"McLeish","year":"1977","journal-title":"The Annals of Probability"},{"key":"S0266466617000500_ref3","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.jkss.2011.07.004","article-title":"Discussion: Bootstrap methods for dependent data: A review","volume":"40","author":"Dahlhaus","year":"2011","journal-title":"Journal of the Korean Statistical Society"},{"key":"S0266466617000500_ref11","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1017\/S0266466602186051","article-title":"The bootstrap of the mean for dependent heterogeneous arrays","volume":"18","author":"Gon\u00e7alves","year":"2002","journal-title":"Econometric Theory"},{"key":"S0266466617000500_ref24","first-page":"263","volume-title":"Exploring the Limits of Bootstrap","author":"Politis","year":"1992"},{"key":"S0266466617000500_ref22","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1214\/07-AOS567","article-title":"A note on the stationary bootstrap\u2019s variance","volume":"37","author":"Nordman","year":"2009","journal-title":"The Annals of Statistics"},{"key":"S0266466617000500_ref25","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1080\/01621459.1994.10476870","article-title":"The stationary bootstrap","volume":"89","author":"Politis","year":"1994","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466617000500_ref4","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0167-7152(93)90134-5","article-title":"An L1-convergence theorem for heterogeneous mixingale arrays with trending moments","volume":"16","author":"Davidson","year":"1993","journal-title":"Statistics and Probability Letters"},{"key":"S0266466617000500_ref16","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.jkss.2011.08.007","article-title":"Rejoinder: Bootstrap methods for dependent data: A review","volume":"40","author":"Kreiss","year":"2011b","journal-title":"Journal of the Korean Statistical Society"},{"key":"S0266466617000500_ref17","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1214\/aos\/1176347265","article-title":"The jackknife and the bootstrap for general stationary observations","volume":"17","author":"Kunsch","year":"1989","journal-title":"The Annals of Statistics"},{"key":"S0266466617000500_ref8","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/B978-044451378-6\/50029-6","volume-title":"Recent Advances and Trends in Nonparametric Statistics","author":"Dowla","year":"2003"},{"key":"S0266466617000500_ref18","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1214\/aos\/1018031117","article-title":"Theoretical comparisons of block bootstrap methods","volume":"27","author":"Lahiri","year":"1999","journal-title":"The Annals of Statistics"},{"key":"S0266466617000500_ref2","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1214\/aoms\/1177700053","article-title":"Moments of randomly stopped sums","volume":"36","author":"Chow","year":"1965","journal-title":"The Annals of Mathematical Statistics"},{"key":"S0266466617000500_ref20","first-page":"165","article-title":"Invariance principles for dependent variables","volume":"32","author":"McLeish","year":"1975","journal-title":"Probability Theory and Related Fields"},{"key":"S0266466617000500_ref14","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.jkss.2011.07.001","article-title":"Discussion: Bootstrap methods for dependent data: A review","volume":"40","author":"Jentsch","year":"2011","journal-title":"Journal of the Korean Statistical Society"},{"key":"S0266466617000500_ref26","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0167-7152(95)00085-2","article-title":"The bootstrap of the mean for strong mixing sequences under minimal conditions","volume":"28","author":"Radulovi\u0107","year":"1996","journal-title":"Statistics and Probability Letters"},{"key":"S0266466617000500_ref1","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1111\/j.1467-9892.1994.tb00204.x","article-title":"Least squares estimation of a shift in linear processes","volume":"15","author":"Bai","year":"1994","journal-title":"Journal of Time Series Analysis"},{"key":"S0266466617000500_ref12","volume-title":"Martingale Limit Theory and its Application","author":"Hall","year":"1980"},{"key":"S0266466617000500_ref27","volume-title":"Asymptotic Statistics","author":"Van der Vaart","year":"2000"},{"key":"S0266466617000500_ref13","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.jkss.2011.07.002","article-title":"Discussion: Bootstrap methods for dependent data: A review","volume":"40","author":"Horowitz","year":"2011","journal-title":"Journal of the Korean Statistical Society"},{"key":"S0266466617000500_ref10","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/j.jkss.2011.07.003","article-title":"Discussion: Bootstrap methods for dependent data: A review","volume":"40","author":"Gon\u00e7alves","year":"2011","journal-title":"Journal of the Korean Statistical Society"},{"key":"S0266466617000500_ref19","first-page":"225","volume-title":"Exploring the Limits of Bootstrap","author":"Liu","year":"1992"},{"key":"S0266466617000500_ref23","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1016\/S1631-073X(02)02578-5","article-title":"Local block bootstrap","volume":"335","author":"Paparoditis","year":"2002","journal-title":"Comptes Rendus Mathematique"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466617000500","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,12]],"date-time":"2020-12-12T01:00:39Z","timestamp":1607734839000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466617000500\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,1]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["S0266466617000500"],"URL":"https:\/\/doi.org\/10.1017\/s0266466617000500","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,1]]},"assertion":[{"value":"Copyright \u00a9 Cambridge University Press 2018\u00a0","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}