A new parametric model, likelihood methods, and other advancements for multivariate extremes

新的参数模型、似然方法和多元极值的其他进步

• 批准号: 2311164
• 负责人: Daniel Cooley
• 金额: $ 30万
• 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: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311164&HistoricalAwards=false
• 关键词: new; parametric; model; likelihood; methods

Understanding extremal dependence in high dimensions is essential for quantifying risk arising from a combination of multiple factors in a variety of disciplines including the environmental and climate sciences. When dependence is described by covariance, many statistical methods exist to characterize and model structure for high-dimensional data. Covariance, however, is a poor descriptor of a distribution's joint tail and methods specifically designed for extremes are necessary for accurate quantification of joint risk. While theoretically-justified frameworks for describing extremal dependence are known, statistical methods for high dimensional extremes are very much needed by practitioners. Building on the investigator's previous work, this project will present and develop the properties of a new multivariate distribution for extremes. The distribution is characterized by a parameter matrix which summarizes pairwise tail dependencies like a covariance matrix, but which is linked to a theoretically-justified framework for extremes. This distribution, coupled with tools in development by the investigator, will allow a practitioner to model and characterize risk for high dimensional data arising in finance, insurance, or meteorological applications. The project will also involve training a graduate student in extreme value analysis and collaboration with atmospheric scientists in government labs.In more detail, recent work on transformed-linear models for extremes coupled with characterizing extremal dependence via the tail pairwise dependence matrix (TPDM) has built connections between extremes modeling and traditional linear statistics methods. Extremal analogues to principal component analysis, spatial autoregressive models, linear autoregressive moving average (ARMA) time series models, linear prediction, and partial correlation have been constructed. However, parameter estimation has thus far been somewhat ad-hoc, and has been based minimizing squared differences between the model's TPDM values and empirical estimates. This project presents a new probability distribution, the transformed-linear T-distribution, which has the TPDM as a parameter. As this distribution has a closed-form density, it makes likelihood estimation of the TPDM possible. Additionally, this project will extend the investigator's recent linear time series work to build non-causal models, as the causal analogs to classical ARMA models show an asymmetry not seen in the data. This project will also extend the recent partial tail correlation work to add causal direction to the graphical models.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.

在高维度中了解极端依赖性对于量化各种学科中多个因素（包括环境和气候科学）中多个因素的结合而产生的风险至关重要。 当通过协方差描述依赖性时，存在许多统计方法来表征高维数据的模型结构。 但是，协方差是分布关节尾的差描述符，专门针对极端设计的方法对于准确量化关节风险是必要的。 尽管已知用于描述极端依赖性的理论上约束的框架是已知的，但从业者非常需要高维极端的统计方法。 在调查员以前的工作的基础上，该项目将介绍并开发新的多元分布的属性。 该分布的特征是参数矩阵，该参数矩阵总结了成对的尾部依赖性，例如协方差矩阵，但与理论上正式的极端框架相关。 这种分布，加上研究人员的开发工具，将使从业者对金融，保险或气象应用中产生的高维数据的风险进行建模并表征。该项目还将涉及培训一名研究生进行极端价值分析，并与政府实验室中的大气科学家进行合作。从更详细的角度来看，最新的关于极端变换的线性模型的工作，以及通过尾部成对依赖矩阵（TPDM）在极端建模和传统线性统计方法之间建立了连接的极端依赖性。已经构建了对主要组件分析，空间自回归模型，线性自回归移动平均（ARMA）时间序列模型，线性预测和部分相关性的极端类似物。但是，到目前为止，参数估计已经有些临时，并且一直基于最小化模型TPDM值和经验估计值之间的平方差异。 该项目提出了一个新的概率分布，即转换的线性T-D-DISTRITUCTION，其将TPDM作为参数。 由于该分布具有封闭形式的密度，因此可能使TPDM的可能性估计。 此外，该项目将将研究者最近的线性时间序列工作扩展到构建非因果模型，因为与经典ARMA模型的因果类似物显示了数据中未见的不对称性。 该项目还将扩展最新的部分尾巴相关工作，以将因果方向增加图形模型。该奖项反映了NSF的法定任务，并认为使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估。