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How to estimate the memory of the Elephant Random Walk

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBERCU, Bernard
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorLAULIN, Lucile
dc.date.accessioned2024-04-04T02:43:24Z
dc.date.available2024-04-04T02:43:24Z
dc.date.issued2022-11-01
dc.identifier.issn0361-0926
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191332
dc.description.abstractEnWe introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more than a quasi-maximum likelihood estimator, based on a second order Taylor approximation of the log-likelihood function. We show the almost sure convergence of our estimate in the diffusive, critical and superdiffusive regimes. The local asymptotic normality of our statistical procedure is established in the diffusive regime, while the local asymptotic mixed normality is proven in the superdiffusive regime. Asymptotic and exact confidence intervals as well as statistical tests are also provided. All our analysis relies on asymptotic results for martingales and the quadratic variations associated.
dc.language.isoen
dc.publisherTaylor & Francis
dc.subject.enElephant random walk
dc.subject.enMaximum likelihood estimation
dc.subject.enAlmost sure convergence
dc.subject.enLocal asymptotic normality
dc.title.enHow to estimate the memory of the Elephant Random Walk
dc.typeArticle de revue
dc.identifier.doi10.1080/03610926.2022.2139149
dc.subject.halMathématiques [math]/Statistiques [math.ST]
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halPhysique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an]
dc.identifier.arxiv2112.10405
bordeaux.journalCommunications in Statistics - Theory and Methods
bordeaux.page1-21
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03483257
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03483257v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Statistics%20-%20Theory%20and%20Methods&rft.date=2022-11-01&rft.spage=1-21&rft.epage=1-21&rft.eissn=0361-0926&rft.issn=0361-0926&rft.au=BERCU,%20Bernard&LAULIN,%20Lucile&rft.genre=article


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