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Adaptive estimation for bifurcating Markov chains

dc.contributor.authorHoffmann, Marc
dc.contributor.authorOlivier, Adélaïde
dc.contributor.authorValère Bitseki Penda, Siméon
dc.date.accessioned2017-11-30T10:12:28Z
dc.date.available2017-11-30T10:12:28Z
dc.date.issued2017
dc.identifier.issn1350-7265
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17112
dc.language.isoenen
dc.subjectBinary trees
dc.subjectBifurcating Markov chains
dc.subjectNonparametric adaptive estimation
dc.subjectBifurcating autoregressive process
dc.subjectGrowth-fragmentation processes
dc.subjectMinimax rates of convergence
dc.subjectDeviations inequalities
dc.subject.ddc519en
dc.titleAdaptive estimation for bifurcating Markov chains
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric wavelet thresholding estimation procedures: in a second part, we construct nonparametric estimators of the transition density of a BMC, of its mean transition density and of the corresponding invariant density, and show smoothness adaptation over various multivariate Besov classes under $L^p$ -loss error, for $1\leq p<\infty$. We prove that our estimators are (nearly) optimal in a minimax sense. As an application, we obtain new results for the estimation of the splitting size-dependent rate of growth-fragmentation models and we extend the statistical study of bifurcating autoregressive processes.
dc.relation.isversionofjnlnameBernoulli
dc.relation.isversionofjnlvol23
dc.relation.isversionofjnlissue4B
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages3598 - 3637
dc.relation.isversionofdoi10.3150/16-BEJ859
dc.relation.isversionofjnlpublisherInternational Statistical Institute
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-12-15T15:05:50Z


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