no. 6
Statistics
Multi-parameter auto-models with applications to cooperative systems
[Auto-modèles à paramètres multiples et applications aux systèmes coopératifs]

Présenté par : Paul Deheuvels

Hardouin, Cécile1 ; Yao, Jian-Feng2
1 SAMOS-MATISSE, CES, UMR 8174 Université de Paris 1, 90, rue de Tolbiac, 75634 Paris cedex 13, France
2 IRMAR, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France
Comptes Rendus. Mathématique, Tome 345 (2007) no. 6, pp. 349-352.

Nous proposons dans ce travail une extension des auto-modèles de Besag aux familles exponentielles de paramètres multiples. Cette extension est nécessaire dans plusieurs applications comme la construction des modèles coopératifs dont les lois conditionnelles sont des lois Beta.

We propose in this Note an extension of Besag's auto-models to exponential families with multi-dimensional parameters. This extension is necessary for the treatment of spatial models like the ones with Beta conditional distributions. A family of cooperative auto-models is proposed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.019
Hardouin, Cécile 1 ; Yao, Jian-Feng 2

1 SAMOS-MATISSE, CES, UMR 8174 Université de Paris 1, 90, rue de Tolbiac, 75634 Paris cedex 13, France
2 IRMAR, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France 
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Hardouin, Cécile; Yao, Jian-Feng. Multi-parameter auto-models with applications to cooperative systems. Comptes Rendus. Mathématique, Tome 345 (2007) no. 6, pp. 349-352. doi : 10.1016/j.crma.2007.07.019. http://www.numdam.org/articles/10.1016/j.crma.2007.07.019/

[1] Arnold, B.C.; Castillo, E.; Sarabia, J.M. Conditional Specification of Statistical Models, Springer-Verlag, New York, 1999

[2] Besag, J. Spatial interactions and the statistical analysis of lattice systems, J. Roy. Statist. Soc. B, Volume 148 (1974), pp. 1-36

[3] Comets, F. On consistency of a class of estimators for exponential families of Markov random fields on the lattice, Ann. Statist., Volume 20 (1992), pp. 455-468

[4] Comets, F.; Janzura, M. A central limit theorem for conditionally centered random fields with an application to Markov random fields, J. Appl. Prob., Volume 35 (1998), pp. 608-621

[5] Guyon, X. Random Fields on a Network: Modeling, Statistics, and Applications, Springer-Verlag, New York, 1995

[6] Kaiser, M.S.; Cressie, N.; Lee, J. Spatial mixture models based on exponential family conditional distributions, Statistica Sinica, Volume 12 (2002), pp. 449-474

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