On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Quality control and dynamic reliability [CQFD] | |
| dc.contributor.author | BERCU, Bernard | |
| hal.structure.identifier | Institut de Mathématiques de Bourgogne [Dijon] [IMB] | |
| dc.contributor.author | CÉNAC, Peggy | |
| hal.structure.identifier | Informatique, Mathématiques et Automatique pour la Route Automatisée [IMARA] | |
| dc.contributor.author | FAYOLLE, Guy | |
| dc.date.accessioned | 2024-04-04T02:43:24Z | |
| dc.date.available | 2024-04-04T02:43:24Z | |
| dc.date.issued | 2008 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191333 | |
| dc.description.abstractEn | We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of any even order converge in the almost sure cental limit theorem for martingales. A conjecture about almost sure upper bounds under wider hypotheses is formulated. The theoretical results are supported by examples borrowed from statistical applications, including linear autoregressive models and branching processes with immigration, for which new asymptotic properties are established on estimation and prediction errors. | |
| dc.language.iso | en | |
| dc.subject.en | Almost sure central limit theorem | |
| dc.subject.en | vector martingale | |
| dc.subject.en | moment | |
| dc.subject.en | stochastic regression | |
| dc.title.en | On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications | |
| dc.type | Rapport | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 0812.3528 | |
| bordeaux.page | 26 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.type.institution | INRIA | |
| bordeaux.type.report | rr | |
| hal.identifier | inria-00348138 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00348138v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2008&rft.spage=26&rft.epage=26&rft.au=BERCU,%20Bernard&C%C3%89NAC,%20Peggy&FAYOLLE,%20Guy&rft.genre=unknown |
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