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| HAL : hal-00154382, version 1 |
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| Biometrika 95 (2008) 335-349 |
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| Multi-parameter auto-models and their application |
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| Cécile Hardouin 1, 2Jian-Feng Yao 3 |
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| (2008) |
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| Motivated by the modelling of non Gaussian data or positively correlated data on a lattice, extensions of Besag's Markov random fields auto-models to exponential families with multi-dimensional parameters have been proposed recently. In this paper, we provide a multiple-parameter analog of Besag's one-dimensional result that gives the necessary form of the exponential families for the Markov random field's conditional distributions. We propose estimation of parameters by maximum pseudo-likelihood and give a proof for the consistency of the estimators for the multi-parameter auto-model. The methodology is illustrated with some examples, particularly the building of a cooperative system with beta conditional distributions. |
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| 1 : | Statistique Appliquée et MOdélisation Stochastique (SAMOS) |
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Université Panthéon-Sorbonne - Paris I |
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| 2 : | Centre d'économie de la Sorbonne (CES) |
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CNRS : UMR8174 – Université Panthéon-Sorbonne - Paris I |
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| 3 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes I – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées de Rennes |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Auto-models – Multi-parameter exponential families – spatial cooperation – beta conditionals |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00154382, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00154382/fr/ | |
| oai:hal.archives-ouvertes.fr:hal-00154382_v1 | |
| Contributeur : Jian-Feng Yao | |
| Soumis le : Mercredi 13 Juin 2007, 14:25:29 | |
| Dernière modification le : Vendredi 19 Mars 2010, 09:41:34 | |
