FRG: Collaborative Research: Extreme value theory for spatially indexed functional data

FRG：协作研究：空间索引函数数据的极值理论

基本信息

批准号：
1462368
负责人：
Stilian Stoev
金额：
$ 24.97万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-08-01 至 2018-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1462368&HistoricalAwards=false
关键词：
FRG Collaborative Research Extreme value

项目摘要

This project focuses on the development of statistical tools to model the spatial and temporal structure of environmental and climate extreme events. Most climate and environmental data sets can be viewed as collections of curves, one curve per year, available at several locations within a region. For example, temperature at a specific location has an annual pattern. The shapes of such annual curves change from year to year, and from location to location. Extreme departures from a typical pattern over a sizeable region can impact agricultural production and public health. The economic impacts are considerable, particularly, if they occur at unexpected times and locations. An unusual timing of a heat wave over a large area may cause significant economic damage due to crop failure and forest fires, and also affect the level of preparedness of public health services. Similarly, long spells of cold, storm-free winter time weather often lead to an increase in particulate pollution levels in densely populated mountain valleys. It is important that public officials are well-informed about the possible range and impact of such extreme events. This project will contribute toward a rigorous and objective understanding of the risks involved, and provide quantitative tools for researchers and decision makers in the fields of agriculture, public health, actuarial science, climatology and ecology.The project seeks to develop a statistical framework for a quantitative assessment of possible extremal departures from the usual annual pattern over a region, i.e. departures of the form that have not been observed in historical records, but can occur with a positive probability. The primary focus of the project is the creation of a mathematical framework, and implementation through the development of statistical software. Building on recent advances in functional data analysis, extreme value theory and spatio-temporal statistics, methodology for modeling the extremal distributions of curves observed at spatial locations will be developed. Extreme curves will be determined by functionals defined on a function space in which the curves live. The work will be guided and validated by the analysis of several historical, derived, and computer data sets. Exploratory analysis will reveal the most prominent properties of extremal shapes. This will be followed by model building and the development of asymptotic theory needed to evaluate probabilities of events not previously observed. The models will reveal extremal features of the spatially indexed functional data that are not apparent from the exploratory analysis. Procedures for the construction of confidence regions, where extremal departures may occur with prescribed probability, will be obtained. Exploratory and inferential tools for the assessment of trends in the extremal shapes and regions over which they occur will also be derived.

该项目着重于开发统计工具，以模拟环境和气候极端事件的空间和时间结构。大多数气候和环境数据集可以看作是曲线的集合，每年一条曲线，在一个地区的几个位置可用。例如，特定位置的温度具有年度模式。这种年度曲线的形状每年都会变化，从地点到位置。在较大地区的典型模式极端偏离会影响农业生产和公共卫生。经济影响是相当大的，特别是如果它们发生在意外的时间和地点。热浪在大面积上的异常时机可能会因作物衰竭和森林大火而造成严重的经济损害，并影响公共卫生服务的准备水平。同样，长期的冷，无暴风雨的冬季天气通常会导致人口稠密的山谷的颗粒污染水平增加。重要的是，公职人员对此类极端事件的可能范围和影响有很好的信息。该项目将有助于对所涉及风险的严格和客观理解，并为农业，公共卫生，精神科学，气候和生态学领域的研究人员和决策者提供定量工具。该项目旨在为一个统计框架开发一个统计框架定量评估可能的极端偏离一个地区通常的年度模式，即在历史记录中未观察到的形式的偏离，但可能以积极的概率发生。该项目的主要重点是创建数学框架，并通过开发统计软件来实现。基于功能数据分析，极值理论和时空统计的最新进展，将开发用于建模在空间位置观察到的曲线极端分布的方法。极端曲线将由在曲线实时的功能空间上定义的功能确定。这项工作将通过对几个历史，派生和计算机数据集的分析来指导和验证。探索性分析将揭示极端形状最突出的特性。之后，模型构建以及评估以前未观察到的事件的概率所需的渐近理论的发展。这些模型将揭示空间索引功能数据的极端特征，这些功能数据从探索性分析中不明显。将获得置信区域建设的程序，其中可能会以规定的概率发生极端出发。还将得出探索性和推论工具，用于评估它们发生的极端形状和区域的趋势。