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Biometrika Advance Access originally published online on April 30, 2008
Biometrika 2008 95(2):335-349; doi:10.1093/biomet/asn016
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© 2008 Biometrika Trust

Articles

Multi-parameter automodels and their applications

Cécile Hardouin

Statistique Appliquée et Modélisation Stochastique, Centre d'Economie de la Sorbonne, Université Paris 1, 90 rue de Tolbiac, 75634 Paris Cedex 13, France
hardouin{at}univ-paris1.fr

Jian-Feng Yao

Institut de Recherche Mathématique de Rennes, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France
jian-feng.yao{at}univ-rennes1.fr

Received for publication 1 February 2007. Revision received 1 October 2007.
  Abstract

Motivated by the modelling of non-Gaussian data or positively correlated data on a lattice, extensions of Besag's automodels to exponential families with multi-dimensional parameters have been proposed recently. We provide a multiple-parameter analogue 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 pseudolikelihood and give a proof of the consistency of the estimators for the multi-parameter automodel. The methodology is illustrated with examples, in particular the building of a cooperative system with beta conditional distributions. We also indicate future applications of these models to the analysis of mixed-state spatial data.

Key Words: Automodel • Beta conditional • Multi-parameter exponential family • Spatial cooperation


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