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DOI: 10.1093/biomet/asn016

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Biometrika 95, 2 (2008) 335-349

Multi-parameter auto-models and their application

Cécile Hardouin 1, 2, Jian-Feng Yao 3

(2008-06)

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.

1:	Statistique Appliquée et MOdélisation Stochastique (SAMOS)
	Université Paris I - Panthéon-Sorbonne
2:	Centre d'économie de la Sorbonne (CES)
	CNRS : UMR8174 – Université Paris I - Panthéon-Sorbonne
3:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): Auto-models – Multi-parameter exponential families – spatial cooperation – beta conditionals

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From: Jian-Feng Yao <>

Submitted on: Wednesday, 13 June 2007 14:25:29

Updated on: Tuesday, 27 April 2010 17:35:08