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Asymptotic analysis for bifurcating autoregressive processes via a martingale approach

hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBERCU, Bernard
hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierGroupe de Recherche en Economie Théorique et Appliquée [GREThA]
dc.contributor.authorDE SAPORTA, Benoîte
hal.structure.identifierQuality control and dynamic reliability [CQFD]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorGEGOUT-PETIT, Anne
dc.date.accessioned2024-04-04T02:50:01Z
dc.date.available2024-04-04T02:50:01Z
dc.date.created2008-07-03
dc.date.issued2009-11-11
dc.identifier.issn1083-6489
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191873
dc.description.abstractEnWe study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.
dc.language.isoen
dc.publisherInstitute of Mathematical Statistics (IMS)
dc.subject.enbifurcating autoregressive process
dc.subject.entree-indexed times series
dc.subject.enmartingales
dc.subject.enleast squares estimation
dc.subject.enalmost sure convergence
dc.subject.enquadratic strong law
dc.subject.encentral limit theorem
dc.title.enAsymptotic analysis for bifurcating autoregressive processes via a martingale approach
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halMathématiques [math]/Statistiques [math.ST]
dc.subject.halStatistiques [stat]/Théorie [stat.TH]
dc.identifier.arxiv0807.0528
bordeaux.journalElectronic Journal of Probability
bordeaux.page2492-2526
bordeaux.volume14
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue87
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00293341
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00293341v1
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