Statistical inference for max-stable processes in space and time

• 成果类型: Article
• 署名作者: Davis, Richard A.; Klueppelberg, Claudia; Steinkohl, Christina
• 署名单位: Columbia University; Technical University of Munich
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12012
• 发表日期: 2013
• 页码: 791-819
• 关键词: pairwise likelihood; FIELDS

摘要

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several families of max-stable random fields have been proposed in the literature. One such representation is based on a limit of normalized and rescaled pointwise maxima of stationary Gaussian processes that was first introduced by Kabluchko and co-workers. This paper deals with statistical inference for max-stable space-time processes that are defined in an analogous fashion. We describe pairwise likelihood estimation, where the pairwise density of the process is used to estimate the model parameters. For regular grid observations we prove strong consistency and asymptotic normality of the parameter estimates as the joint number of spatial locations and time points tends to . Furthermore, we discuss extensions to irregularly spaced locations. A simulation study shows that the method proposed works well for these models.