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dc.contributor.authorBelloni, Alexandre
dc.contributor.authorChernozhukov, Victor V.
dc.date.accessioned2013-09-26T15:17:18Z
dc.date.available2013-09-26T15:17:18Z
dc.date.issued2009-08
dc.date.submitted2008-06
dc.identifier.issn0090-5364
dc.identifier.urihttp://hdl.handle.net/1721.1/81193
dc.description.abstractIn this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace–Bernstein–Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using the conditions required for the central limit theorem to hold, we establish polynomial bounds on the computational complexity of general Metropolis random walks methods in large samples. Our analysis covers cases where the underlying log-likelihood or extremum criterion function is possibly nonconcave, discontinuous, and with increasing parameter dimension. However, the central limit theorem restricts the deviations from continuity and log-concavity of the log-likelihood or extremum criterion function in a very specific manner. Under minimal assumptions required for the central limit theorem to hold under the increasing parameter dimension, we show that the Metropolis algorithm is theoretically efficient even for the canonical Gaussian walk which is studied in detail. Specifically, we show that the running time of the algorithm in large samples is bounded in probability by a polynomial in the parameter dimension d and, in particular, is of stochastic order d2 in the leading cases after the burn-in period. We then give applications to exponential families, curved exponential families and Z-estimation of increasing dimension.en_US
dc.description.sponsorshipAlfred P. Sloan Foundation (Research Fellowship)en_US
dc.description.sponsorshipNational Science Foundation (U.S.)en_US
dc.description.sponsorshipIBM Research (IBM Herman Goldstein Fellowship)en_US
dc.description.sponsorshipMassachusetts Institute of Technology. Dept. of Economics (Castle Krob Chair)en_US
dc.language.isoen_US
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1214/08-aos634en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceInstitute of Mathematical Statisticsen_US
dc.titleOn the computational complexity of MCMC-based estimators in large samplesen_US
dc.typeArticleen_US
dc.identifier.citationBelloni, Alexandre, and Victor Chernozhukov. “On the computational complexity of MCMC-based estimators in large samples.” The Annals of Statistics 37, no. 4 (August 2009): 2011-2055. © 2009 Institute of Mathematical Statistics.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Economicsen_US
dc.contributor.mitauthorChernozhukov, Victor V.en_US
dc.relation.journalAnnals of Statisticsen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsBelloni, Alexandre; Chernozhukov, Victoren_US
dc.identifier.orcidhttps://orcid.org/0000-0002-3250-6714
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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