{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T13:23:52Z","timestamp":1791638632020,"version":"4.3.4"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[1998,4,1]],"date-time":"1998-04-01T00:00:00Z","timestamp":891388800000},"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":[[1998,4]]},"abstract":"<jats:p>We obtain new central limit theorems (CLT's) \nand functional central limit theorems (FCLT's) for \nHilbert-valued arrays near epoch dependent on mixing processes, \nand also new FCLT's for general Hilbert-valued adapted \ndependent heterogeneous arrays. These theorems are useful \nin delivering asymptotic distributions for parametric and \nnonparametric estimators and their functionals in time \nseries econometrics. We give three significant applications \nfor near epoch dependent observations: (1) A new CLT for \nany plug-in estimator of a cumulative distribution function \n(c.d.f.) (e.g., an empirical c.d.f., or a c.d.f. estimator \nbased on a kernel density estimator), which can in turn \ndeliver distribution results for many Von Mises functionals; \n(2) a new limiting distribution result for degenerate <jats:italic>U<\/jats:italic>-statistics, \nwhich delivers distribution results for Bierens's \nintegrated conditional moment tests; (3) a new functional \ncentral limit result for Hilbert-valued stochastic approximation \nprocedures, which delivers distribution results for nonparametric \nrecursive generalized method of moment estimators, including \nnonparametric adaptive learning models.<\/jats:p>","DOI":"10.1017\/s0266466698142056","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:47:49Z","timestamp":1027777669000},"page":"260-284","source":"Crossref","is-referenced-by-count":57,"title":["CENTRAL LIMIT AND FUNCTIONAL CENTRAL LIMIT THEOREMS FOR \nHILBERT-VALUED DEPENDENT HETEROGENEOUS ARRAYS WITH APPLICATIONS"],"prefix":"10.1017","volume":"14","author":[{"given":"Xiaohong","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Halbert","family":"White","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[1998,4,1]]},"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466698142056","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T19:38:11Z","timestamp":1553888291000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466698142056\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,4]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1998,4]]}},"alternative-id":["S0266466698142056"],"URL":"https:\/\/doi.org\/10.1017\/s0266466698142056","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,4]]}}}