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Laboratoire de Mathématiques Jean Leray UMR 6629 |
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Laboratoire de Mathématiques Jean Leray UMR 6629 |
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| HAL : hal-00502004, version 2 |
| arXiv : 1007.3351 |
| DOI : 10.1111/j.1467-9469.2011.00738.x |
| Fiche détaillée |  Récupérer au format |
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| Scandinavian Journal of Statistics (2012) online: 12 JUL 2011 |
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| Versions disponibles : | v1 (20-07-2010) | v2 (06-01-2011) |
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| Takacs Fiksel method for stationary marked Gibbs point processes |
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| Jean-François Coeurjolly 1, 2David Dereudre 3 |
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| (2012) |
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| This paper studies a method to estimate the parameters governing the distribution of a stationary marked Gibbs point process. This procedure, known as the Takacs-Fiksel method, is based on the estimation of the left and right hand sides of the Georgii-Nguyen-Zessin formula and leads to a family of estimators due to the possible choices of test functions. We propose several examples illustrating the interest and flexibility of this procedure. We also provide sufficient conditions based on the model and the test functions to derive asymptotic properties (consistency and asymptotic normality) of the resulting estimator. The different assumptions are discussed for exponential family models and for a large class of test functions. A short simulation study is proposed to assess the correctness of the methodology and the asymptotic results. |
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| 1 : | Grenoble Images Parole Signal Automatique (GIPSA-lab) |
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CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| 2 : | Laboratoire Jean Kuntzmann (LJK) |
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CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| 3 : | Laboratoire de Mathématiques et leurs Applications de Valenciennes, EA 45 (LAMAV) |
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Université de Valenciennes et du Hainaut-Cambresis – CNRS : FRE2956 |
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| 4 : | Laboratoire de Mathématiques Jean Leray (LMJL) |
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CNRS : UMR6629 – Université de Nantes – École Centrale de Nantes |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| stationary marked Gibbs point processes – parametric estimation – Takacs-Fiksel method – asymptotic properties – ergodic theorem – central limit theorem |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00502004, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00502004 | |
| oai:hal.archives-ouvertes.fr:hal-00502004 | |
| Contributeur : Jean-François Coeurjolly | |
| Soumis le : Jeudi 6 Janvier 2011, 11:03:07 | |
| Dernière modification le : Vendredi 16 Mars 2012, 15:44:03 | |
