Multivariate Dependence Modeling with Copulas

使用 Copula 进行多元依赖建模

• 批准号: RGPIN-2015-06801
• 负责人: Neslehova, Johanna
• 金额: $ 2.26万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=683992
• 关键词: Multivariate; Dependence; Modeling; Copulas

The proposed research focuses on new statistical methodology for copula-based dependence models, which are now widely used in many fields, including environmental and health sciences, finance, insurance, and risk management. Dependence in multivariate data is a complex phenomenon and copula-based models are far more capable of accounting for it than traditional multivariate distributions. My research program is a continuation of my previous NSERC Discovery Grant, with a new focus on complex data structures and recent challenges in applications, such as high-dimensional data, discontinuous variables, or low-probability, high-impact events.***There is a pressing need for versatile yet tractable multivariate copula models that are well suited for the treatment of high-dimensional data. I will devise such models using stochastic representations, develop statistical methodology for them, and make this new methodology available to end-users of statistics through the R Project for Statistical Computing. I will also use the new models to build hierarchical dependence structures for clustered data. Another part of my research will focus on the modeling of dependence between extreme events: I will develop novel statistical techniques based on constrained B-spline estimation; the estimators will correspond to genuine models from which it is possible to simulate and predict catastrophic events. Moreover, I will further my work on empirical copula processes for non-continuous data. This work will serve as a basis for valid statistical methodology for copula-based models for variables that are discrete, mixed or otherwise discontinuous. These new techniques will also be investigated in settings where the number of variables is large; the aim will be to devise graphical tools for the visualization of dependence in high-dimensional data. My methodological work will be applied to various practical problems, e.g., in hydrology, insurance, and risk management.***The impact of the work will be to change the manner in which researchers model multivariate data. It will demonstrate the usefulness of copula-based techniques, and its feasibility even for complex data structures. The research will contribute to the growing literature on high-dimensional dependence modeling, which is of interest to a wide statistical audience. Given the importance of dependence-related issues in fields such as finance, insurance, hydrology, and risk management, the work will have parallel impact in these areas. New methodology will be made accessible to practitioners through the R Project for Statistical Computing.***

拟议的研究重点是基于 copula 的依赖模型的新统计方法，该模型现已广泛应用于许多领域，包括环境和健康科学、金融、保险和风险管理。多元数据中的依赖性是一种复杂的现象，基于联结的模型比传统的多元分布更能解释它。我的研究项目是我之前的 NSERC 发现资助项目的延续，新的重点是复杂的数据结构和应用中的最新挑战，例如高维数据、不连续变量或低概率、高影响的事件。***迫切需要通用且易于处理的多元 copula 模型，这些模型非常适合处理高维数据。我将使用随机表示设计此类模型，为其开发统计方法，并通过 R 统计计算项目向统计最终用户提供这种新方法。我还将使用新模型为集群数据构建分层依赖结构。我的研究的另一部分将集中于极端事件之间依赖性的建模：我将开发基于约束 B 样条估计的新颖统计技术；估计器将对应于可以模拟和预测灾难性事件的真实模型。此外，我将进一步研究非连续数据的经验连接过程。这项工作将作为离散、混合或其他不连续变量的基于联结模型的有效统计方法的基础。这些新技术还将在变量数量较多的环境中进行研究；目的是设计图形工具来可视化高维数据中的依赖性。我的方法论工作将应用于各种实际问题，例如水文学、保险和风险管理。***这项工作的影响将是改变研究人员对多元数据进行建模的方式。它将展示基于 copula 的技术的有用性，及其即使对于复杂数据结构的可行性。该研究将为越来越多的高维依赖性建模文献做出贡献，这引起了广泛的统计受众的兴趣。鉴于依赖相关问题在金融、保险、水文和风险管理等领域的重要性，这项工作将对这些领域产生平行影响。新的方法将通过 R 统计计算项目向从业者提供。***