Biometrika Advance Access published online on April 30, 2008
Biometrika, doi:10.1093/biomet/asn016
Articles |
Multi-parameter automodels and their applications
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
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 January 2007. Revision received 1 October 2007.
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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