SPATIAL DEPENDENCE AND SPACE-TIME TREND IN EXTREME EVENTS

• 成果类型: Article
• 署名作者: Einmahl, John H. J.; Ferreira, Ana; de Haan, Laurens; Neves, Claudia; Zhou, Chen
• 署名单位: Tilburg University; Universidade de Lisboa; Universidade de Lisboa; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam; University of Reading; Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2067
• 发表日期: 2022
• 页码: 30-52
• 关键词: tail dependence

摘要

The statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a pseudo-maximum likelihood procedure based on pooling all (non-stationary and dependent) observations. Our leading example and application is rainfall in Northern Germany.