Multi-parameter auto-models and their application

Cécile Hardouin (1, 2) , Jian-Feng Yao (3)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 CES - Centre d'économie de la Sorbonne
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Auto-models; Multi-parameter exponential families; spatial cooperation; beta conditionals

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Cécile Hardouin, Jian-Feng Yao. Multi-parameter auto-models and their application. Biometrika, 2008, 95 (2), pp.335-349. ⟨10.1093/biomet/asn016⟩. ⟨hal-00154382⟩