Extremes Models and Methods from Transformed Linear Operations

变换线性运算的极值模型和方法

基本信息

批准号：
1811657
负责人：
Daniel Cooley
金额：
$ 24.49万
依托单位：
Colorado State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-06-01 至 2022-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811657&HistoricalAwards=false
关键词：
Extremes Models Methods Transformed Linear

项目摘要

Quantification and assessment of risk associated with extreme-in-magnitude and rare events are important in many science, engineering, and business applications. Univariate extremes methods are well-developed, but there is a need for easily implementable statistical methods to describe and model extremal dependence in high dimensions, and in the time series and spatial contexts. Linear statistical methods including traditional multivariate analysis, time series, and spatial statistics are ubiquitous in non-extreme statistics. Recently, the PI and coauthor connected the seemingly disparate areas of linear statistical methods and extreme value analyses by utilizing transformed-linear operations. An extension of this approach will be used to develop methods for analyzing high-dimensional extremal dependence, modeling extremal dependence in time, and modeling spatial extremes. Because the proposed work is inspired by existing linear models and methods in the non-extreme setting, the models and methods will be relatively simple and familiar. This project will produce statistical methods for describing and modeling extremal dependence via applying transformed-linear operations. In a recently submitted paper, the PI and coauthor link linear algebra to regular variation, a widely-used and theoretically-justified framework for extremal dependence, via transformed linear operations. The PI and coauthor obtain a sensible vector space for extremes yielding the notion of basis, propose an extremes analog to the covariance matrix, and perform an eigendecomposition of this matrix useful for understanding high-dimensional tail dependence. This project aims to develop a simple linear model for extreme spatial data, analogous to the spatial autoregressive model in non-extreme spatial statistics, and transformed-linear time series models inspired by familiar ARMA models, but appropriate for extreme time series data. This project will also develop inference procedures for both the spatial and time series models. Furthermore, this project will further develop linear methods for understanding extremal dependence in high dimensions and explore the idea of conditional dependence and independence for extremes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在许多科学，工程和业务应用中，与极端障碍和罕见事件相关的风险量化和评估很重要。单变量极端方法已经发达了，但是需要易于实现的统计方法来描述和模拟高维度以及时间序列和空间环境中的极端依赖性。线性统计方法在内，包括传统的多元分析，时间序列和空间统计数据在非极端统计中无处不在。最近，PI和合着者通过利用转换的线性操作来连接线性统计方法和极值分析的看似不同的领域。这种方法的扩展将用于开发用于分析高维极端依赖性，对极端依赖性建模和对空间极端建模的方法。由于所提出的工作灵感来自非超级设置中现有的线性模型和方法，因此模型和方法将相对简单且熟悉。该项目将通过应用转换的线性操作产生用于描述和建模极端依赖性的统计方法。在最近提交的论文中，PI和合着者链接线性代数与常规变化，这是一个通过转化的线性操作，是一个极端依赖的广泛使用和理论上的框架。 PI和合着者获得了一个明智的矢量空间，用于产生基础概念，提出与协方差矩阵的极端类似物，并对此矩阵进行特征分类，可用于理解高维尾部依赖性。该项目旨在为极端空间数据开发一个简单的线性模型，该模型类似于非极端空间统计中的空间自回归模型，并转换了受熟悉的ARMA模型启发的线性时间序列序列模型，但适用于极端时间序列数据。该项目还将为空间和时间序列模型开发推理程序。此外，该项目将进一步开发线性方法，以理解高维度的极端依赖性，并探讨了极端的条件依赖性和独立性的想法。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来进行评估的。