CONSISTENCY OF LIKELIHOOD ESTIMATION FOR GIBBS POINT PROCESSES

• 成果类型: Article
• 署名作者: Dereudre, David; Lavancier, Frederic
• 署名单位: Universite de Lille; Nantes Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1466
• 发表日期: 2017
• 页码: 744-770
• 关键词: quermass-interaction processes; inference; EQUIVALENCE; ensembles; systems

摘要

Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or nonlinearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consistency of the MLE for all parameters of the Strauss model, the hardcore Strauss model, the Lennard-Jones model and the area-interaction model.