CAREER: Statistical Inference of Tail Dependent Time Series

职业：尾部相关时间序列的统计推断

基本信息

批准号：
2131821
负责人：
Ting Zhang
金额：
$ 40万
依托单位：
University of Georgia Research Foundation Inc
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2131821&HistoricalAwards=false
关键词：
CAREER Statistical Inference Tail Dependent

项目摘要

The project aims to develop a new theoretical framework and statistical inference methods for the analysis of tail dependent time series, and to educate future statisticians and data scientists on its theory and practice. Tail dependent time series, as an emerging data type, has been observed and recognized in various fields including actuarial science, climate science, economics, finance, hydrology, and internet traffic engineering, among others. The task of understanding and appropriately accommodating the phenomenon of tail dependence can be of significant importance to the modeling of extreme events such as earthquakes, hurricanes, and financial crises. The results from the project will make significant impacts in scientific areas such as climate science, economics, actuarial science, finance, hydrology and internet traffic engineering. The proposal also involves an integrated education plan to expose undergraduate and high school students to the topic, to equip graduate and advanced undergraduate students with a desirable level of statistical reasoning and analytical skills for analyzing tail dependent time series, and to mentor doctoral students to become future leaders in the education and research of the area. Existing methods for studying tail dependent time series often rely on certain parametric models for describing the underlying tail dependence structure. This is particularly due to the lack of a convenient and rigorous framework that one can use to obtain desired limit theorems for a general class of tail dependent time series. The project aims to address this fundamental problem by proposing a new framework based on the causal representation and the technique of adversarial tail coupling. Using the newly proposed framework, the project will develop meaningful results toward a tail m-dependent approximation scheme, which can then be used as a powerful tool to obtain limit theorems for statistics of tail dependent data. Compared with the conventional m-dependent approximation, the current setting can be more challenging due to the double asymptotics where the quantile index is allowed to approach either zero or one as the sample size increases to reflect extreme risks. The project will study several statistical inference problems for tail dependent time series, including high quantile estimation and its associated confidence interval construction, tail dependence visualization and testing, inference of extremely high quantiles using the extreme value theory, extensions to high and extremely high quantile regression models, and high-dimensional nonstationary settings. The results to be developed are expected to be useful in identifying undiscovered features in certain climate science and economic data, and applicable to other scientific problems that involve the analysis of tail dependent time series.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.

该项目旨在开发一种新的理论框架和统计推断方法，以分析依赖尾部的时间序列，并教育未来的统计学家和数据科学家的理论和实践。作为一种新兴数据类型，在包括精算科学，气候科学，经济学，金融，水文学和互联网交通工程等各个领域都观察到并认可了尾巴依赖的时间序列。理解和适当适应尾巴依赖现象的任务对于地震，飓风和金融危机等极端事件的建模至关重要。该项目的结果将对气候科学，经济学，精算科学，金融，水文和互联网交通工程等科学领域产生重大影响。该提案还涉及一项综合的教育计划，以使本科和高中生接触该主题，为研究生和高级本科生配备理想水平的统计推理和分析技能，以分析依赖尾巴的时间序列，并指导博士生成为该领域教育和研究的未来领导者。研究依赖尾部时间序列的现有方法通常依赖于某些参数模型来描述潜在的尾部依赖结构。这尤其是由于缺乏方便且严格的框架，可以用来为一般的尾巴依赖时间序列获得所需的限制定理。该项目旨在通过提出基于因果关系和对抗尾耦合技术的新框架来解决这个基本问题。使用新提出的框架，该项目将针对尾部M依赖性近似方案开发有意义的结果，然后可以将其用作有力的工具，以获取限制尾部依赖数据统计的定理。与传统的M依赖性近似相比，由于允许分位数指数允许零或一个接近零或一个，随着样本量增加以反映极端风险，当前设置可能更具挑战性。该项目将研究有关尾部依赖时间序列的几个统计推断问题，包括高分位数估计及其相关的置信区间构建，使用极值理论的尾巴依赖性可视化和测试，对极高的分位数的推断，对高分位数回归模型的扩展以及高维度的非量度非机构环境。预计要开发的结果将有助于确定某些气候科学和经济数据中未发现的特征，并适用于其他科学问题，涉及涉及尾部依赖时间序列的分析。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影响的审查标准来通过评估来支持的。