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Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model

hal.structure.identifierInstitut de Mathématiques de Bourgogne [Dijon] [IMB]
dc.contributor.authorBitseki Penda, Siméon Valère
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorRoche, Angelina
dc.date.accessioned2021-12-13T13:41:12Z
dc.date.available2021-12-13T13:41:12Z
dc.date.issued2020
dc.identifier.issn1048-5252
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22377
dc.language.isoenen
dc.subjectNonparametric kernel estimationen
dc.subjectGoldenshluger-Lepski methodologyen
dc.subjectadaptive estimationen
dc.subjectbinary treesen
dc.subjectbifurcating autoregressive processesen
dc.subject.ddc519en
dc.titleLocal bandwidth selection for kernel density estimation in a bifurcating Markov chain modelen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain onRd. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estimator is proposed whose bandwidths are selected by a method inspired by the works of Goldenshluger and Lepski [(2011), 'Bandwidth Selection in Kernel Density Estimation: Oracle Inequalities and Adaptive Minimax Optimality',The Annals of Statistics3: 1608-1632). Drawing inspiration from dimension jump methods for model selection, we also provide an algorithm to select the best constant in the penalty. Finally, we investigate the performance of the method by simulation studies and application to real data.en
dc.relation.isversionofjnlnameJournal of Nonparametric Statistics
dc.relation.isversionofjnlvol32en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2020-07
dc.relation.isversionofjnlpages535-562en
dc.relation.isversionofdoi10.1080/10485252.2020.1789125en
dc.relation.isversionofjnlpublisherTaylor & Francisen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-12-13T13:38:41Z
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