Comptes Rendus
Statistics
Multi-parameter auto-models with applications to cooperative systems
Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 349-352.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.07.019
Cécile Hardouin 1; Jian-Feng Yao 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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Cécile Hardouin; Jian-Feng Yao. Multi-parameter auto-models with applications to cooperative systems. Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 349-352. doi : 10.1016/j.crma.2007.07.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.019/

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

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

[3] F. Comets 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] F. Comets; M. Janzura 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] X. Guyon Random Fields on a Network: Modeling, Statistics, and Applications, Springer-Verlag, New York, 1995

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

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