Spatial extremes: Models for the stationary case

• 成果类型: Article
• 署名作者: De Haan, L; Pereira, TT
• 署名单位: Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC; Universidade de Lisboa
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000886
• 发表日期: 2006
• 页码: 146-168
• 关键词: stochastic-processes; sample

摘要

The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and Pickands [Probab. Theory Related Fields 72 (1986) 477-492]. We propose three one-dimensional and three two-dimensional models. These models depend on just one parameter or a few parameters that measure the strength of tail dependence as a function of the distance between locations. We also propose two estimators for this parameter and prove consistency under domain of attraction conditions and asymptotic normality under appropriate extra conditions.