Multi-parameter automodels and their applications

• 成果类型: Article
• 署名作者: Hardouin, Cecile; Yao, Jian-Feng
• 署名单位: heSam Universite; Universite Pantheon-Sorbonne; Universite de Rennes
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn016
• 发表日期: 2008
• 页码: 335349
• 关键词: DISTRIBUTIONS; models

摘要

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.