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| HAL : hal-00522842, version 2 |
| arXiv : 1010.0426 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Multivariate Analysis, 105 (2012) 222-240 |
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| Versions disponibles : | v1 (03-10-2010) | v2 (22-09-2011) |
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| Adaptive estimator of the memory parameter and goodness-of-fit test using a multidimensional increment ratio statistic |
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| Jean-Marc Bardet 1Béchir Dola 1 |
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| (2012) |
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| The increment ratio (IR) statistic was first defined and studied in Surgailis {\it et al.} (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. Firstly, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Secondly, a goodness-of-fit $\chi^2$-type test can be deduced from this theorem. Finally, this theorem allows to construct adaptive versions of the estimator and test which are studied in a general semiparametric frame. The adaptive estimator of the long-memory parameter is proved to follow an oracle property. Simulations attest of the interesting accuracies and robustness of the estimator and test, even in the non Gaussian case. |
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| 1 : | Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM) |
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Université Paris I - Panthéon-Sorbonne |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Long-memory Gaussian processes – goodness-of-fit test – estimation of the memory parameter – minimax adaptive estimator. |
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| hal-00522842, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00522842 | |
| oai:hal.archives-ouvertes.fr:hal-00522842 | |
| Contributeur : Jean-Marc Bardet | |
| Soumis le : Jeudi 22 Septembre 2011, 09:12:06 | |
| Dernière modification le : Mardi 26 Février 2013, 19:56:42 | |
