A q-exponential statistical Banach manifold

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dc.citation.journalTitleJournal Of Mathematical Analysis And Applications
dc.contributor.authorLoaiza, G.
dc.contributor.authorQuiceno, H. R.
dc.contributor.departmentUniversidad EAFIT. Departamento de Cienciasspa
dc.contributor.researchgroupMatemáticas y Aplicacionesspa
dc.creatorLoaiza, G.
dc.creatorQuiceno, H. R.
dc.date.accessioned2021-04-12T14:04:17Z
dc.date.available2021-04-12T14:04:17Z
dc.date.issued2013-02-15
dc.description.abstractLet µ be a given probability measure and Mµ the set of µ-equivalent strictly positive probability densities. In this paper we construct a Banach manifold on Mµ, modeled on the space L 8(p{dot operator}µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis's deformed exponential), where 0<q<1 is any real number. This family is characterized by the fact that when q?1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space. The coordinate mappings of the manifold are given in terms of Csiszár's F-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score function. © 2012 Elsevier Ltd.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1318
dc.identifier.doi10.1016/j.jmaa.2012.08.046
dc.identifier.issn0022247X
dc.identifier.issn10960813
dc.identifier.otherWOS;000311330600003
dc.identifier.otherSCOPUS;2-s2.0-84868198129
dc.identifier.urihttp://hdl.handle.net/10784/27679
dc.language.isoengeng
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84868198129&doi=10.1016%2fj.jmaa.2012.08.046&partnerID=40&md5=f7adfc0ef1f7972561897d1d25c967fc
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0022-247X
dc.sourceJournal Of Mathematical Analysis And Applications
dc.subjectDifferentiable mappingseng
dc.subjectDifferential geometryeng
dc.subjectInformation theoryeng
dc.titleA q-exponential statistical Banach manifoldeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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