On prediction of individual sequences
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- dc.contributor.author Cesana Arlotti, Nicolò, 1981-ca
- dc.contributor.author Lugosi, Gáborca
- dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
- dc.date.accessioned 2017-07-26T10:50:00Z
- dc.date.available 2017-07-26T10:50:00Z
- dc.date.issued 1998-07-01
- dc.date.modified 2017-07-23T02:03:57Z
- dc.description.abstract Sequential randomized prediction of an arbitrary binary sequence is investigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimax relative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.
- dc.format.mimetype application/pdfca
- dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=324
- dc.identifier.citation Annals of Statistics, 27, 6, (1999), 1865-1895
- dc.identifier.uri http://hdl.handle.net/10230/1228
- dc.language.iso eng
- dc.relation.ispartofseries Economics and Business Working Papers Series; 324
- dc.rights L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
- dc.subject.keyword universal prediction
- dc.subject.keyword prediction with experts
- dc.subject.keyword absolute loss
- dc.subject.keyword empirical processes
- dc.subject.keyword covering numbers
- dc.subject.keyword finite-state machines
- dc.subject.keyword Statistics, Econometrics and Quantitative Methods
- dc.title On prediction of individual sequencesca
- dc.type info:eu-repo/semantics/workingPaper