How to estimate the memory of the Elephant Random Walk
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BERCU, Bernard | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LAULIN, Lucile | |
| dc.date.accessioned | 2024-04-04T02:43:24Z | |
| dc.date.available | 2024-04-04T02:43:24Z | |
| dc.date.issued | 2022-11-01 | |
| dc.identifier.issn | 0361-0926 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191332 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | Taylor & Francis | |
| dc.subject.en | Elephant random walk | |
| dc.subject.en | Maximum likelihood estimation | |
| dc.subject.en | Almost sure convergence | |
| dc.subject.en | Local asymptotic normality | |
| dc.title.en | How to estimate the memory of the Elephant Random Walk | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1080/03610926.2022.2139149 | |
| dc.subject.hal | Mathématiques [math]/Statistiques [math.ST] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Physique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an] | |
| dc.identifier.arxiv | 2112.10405 | |
| bordeaux.journal | Communications in Statistics - Theory and Methods | |
| bordeaux.page | 1-21 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03483257 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03483257v1 | |
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