FRG: Collaborative Proposal: Extreme Theory Value Theory for Spatially Indexed Functional Data

FRG：协作提案：空间索引函数数据的极端理论价值理论

• 批准号: 1463642
• 负责人: Joshua French
• 金额: $ 12.93万
• 依托单位: University of Colorado at Denver
• 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 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1463642&HistoricalAwards=false
• 关键词: FRG; Collaborative; Proposal; Extreme; Theory

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.

该项目侧重于开发统计工具，以模拟环境和气候极端事件的时空结构。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，可在一个区域内的几个地点获得。例如，特定地点的温度有一个年模式。这种年曲线的形状每年都在变化，也随地点的不同而变化。在一个相当大的区域，与典型模式的极端背离可能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想不到的时间和地点。在不寻常的时间出现大面积热浪，可能会因作物歉收和森林火灾造成重大经济损失，还会影响公共卫生服务的准备水平。同样，长时间的寒冷、无风暴的冬季天气往往会导致人口稠密的山谷中颗粒物污染水平的增加。重要的是，公职人员应充分了解这种极端事件的可能范围和影响。该项目将有助于严格和客观地了解所涉及的风险，并为农业、公共卫生、精算科学、气候学和生态学等领域的研究人员和决策者提供定量工具。该项目力求制定一个统计框架，以定量评估一个区域可能出现的偏离通常年型的极端情况，即在历史记录中没有观察到但有可能出现的偏离形式。该项目的主要焦点是创建一个数学框架，并通过开发统计软件来实现。在功能数据分析、极值理论和时空统计方面的最新进展的基础上，将发展对在空间位置观察到的曲线的极值分布进行建模的方法。极值曲线将由定义在曲线所在函数空间上的函数决定。这项工作将通过对几个历史、衍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。接下来是模型的建立和渐近理论的发展，这需要评估以前未观察到的事件的概率。这些模型将揭示空间索引功能数据的极端特征，这些特征在探索性分析中并不明显。将获得构建置信区域的程序，置信区域的极端偏离可能以规定的概率发生。还将推导出用于评估极端形状及其发生区域的趋势的探索性和推断性工具。

项目成果

Nontuberculous Mycobacterial Disease and Molybdenum in Colorado Watersheds

• DOI: 10.3390/ijerph17113854
• 发表时间: 2020-06-01
• 期刊: INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH
• 作者: Lipner, Ettie M.;French, Joshua;Crooks, James L.
• 通讯作者: Crooks, James L.

A sandwich smoother for spatio-temporal functional data

用于时空函数数据的三明治平滑器

• DOI: 10.1016/j.spasta.2020.100413
• 发表时间: 2020
• 期刊: Spatial Statistics
• 影响因子: 2.3
• 作者: French, Joshua P.;Kokoszka, Piotr S.
• 通讯作者: Kokoszka, Piotr S.