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Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | GÉGOUT-PETIT, Anne | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Groupe de Recherche en Economie Théorique et Appliquée [GREThA] | |
| dc.contributor.author | DE SAPORTA, Benoîte | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BERCU, Bernard | |
| dc.date.accessioned | 2024-04-04T02:46:21Z | |
| dc.date.available | 2024-04-04T02:46:21Z | |
| dc.date.created | 2008-05-30 | |
| dc.date.conference | 2008-05-25 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191543 | |
| dc.description.abstractEn | We study the least-square (LS) estimator of the unknown parameters of a bifurcating auto-regressive process (BAR). Under very weak assumptions on the noise sequence (namely conditional pair-wise independence and moments of order $4$), we derive a precise rate of convergence for the LS estimator, as well as a quadratic strong law and a central limit theorem. Our main tool is martingale theory. However, standard results do not apply directly, as the martingales involved here have a special form and an exponential growth rate. | |
| dc.language.iso | en | |
| dc.subject.en | Bifurcating auto-regression | |
| dc.subject.en | Tree-indexed times series | |
| dc.subject.en | Martingales | |
| dc.subject.en | Least-squares estimator | |
| dc.subject.en | Almost sure convergence | |
| dc.subject.en | Convergence rate | |
| dc.subject.en | Quadratic strong law | |
| dc.subject.en | Central limit theorem | |
| dc.title.en | Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach | |
| dc.type | Communication dans un congrès | |
| dc.subject.hal | Mathématiques [math]/Statistiques [math.ST] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | Joint Meeting of the Statistical Society of Canada and the Société Française de Statistique | |
| bordeaux.country | CA | |
| bordeaux.conference.city | Ottawa | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00325866 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | non | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00325866v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=G%C3%89GOUT-PETIT,%20Anne&DE%20SAPORTA,%20Beno%C3%AEte&BERCU,%20Bernard&rft.genre=unknown |
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