Distributional effects and computational challenges in modern data analysis

现代数据分析中的分布效应和计算挑战

• 批准号: RGPIN-2017-06622
• 负责人: Volgushev, Stanislav
• 金额: $ 2.55万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712283
• 关键词: Distributional; effects; computational; challenges; modern

The research agenda described in this proposal has two main threads: procedures for inference in massive data sets and the use of copulas in time series analysis. With modern data collection techniques, extremely large data sets become more and more prevalent. To extract useful information from such data sets, statistical procedures that can handle large amounts of data and remain computationally feasible need to be developed. This motivates the first research direction: fast bootstrap procedures for massive data sets. The goal of this part of the proposed research is to gain a deep and comprehensive understanding of the limitations associated with bootstrap procedures that are specifically designed for large-scale data sets. This will be achieved by analyzing a wide array of scenarios where the classical bootstrap or modifications thereof are known to be applicable. In cases where the available methods fail, I plan to develop alternative approaches that continue to be applicable. With data sets that are growing at an ever increasing rate, fast and accurate procedures for quantifying uncertainty of statistical procedures are in high demand. My long-term goal is to enable the scientific community to conduct fast and reliable inference for the new type of large and messy data sets that are becoming more and more common in the modern data world. The research described above will provide a first step towards a deep and comprehensive study of such procedures and enable researchers and industry professionals to make full use of the data they collect. The second main topic of this proposal is the use of copulas in time series analysis. Since the financial crisis, it is well known that correct modeling of complex dependencies among economic variables or financial instruments is extremely important. Copulas provide a simple and elegant way to find and validate such models. During the next five years, I aim to extend classical tools from time series analysis to allow visualization and analysis of distributional effects in dynamics of time series by using copulas. To this end I aim to provide the statistical community with a toolbox of methods that are grounded in solid theoretical understanding, well-documented and understandable to the non-technical time series and copula community, and have a fast and reliable implementation in R in order to facilitate the wide-spread use of such methods in a broad community of applied researchers and beyond.

该提案中描述的研究议程有两个主要线索：海量数据集中的推理程序和时间序列分析中联结函数的使用。 随着现代数据收集技术的发展，极大的数据集变得越来越普遍。为了从此类数据集中提取有用的信息，需要开发能够处理大量数据并保持计算可行性的统计程序。这激发了第一个研究方向：海量数据集的快速引导程序。拟议研究的这一部分的目标是深入、全面地了解与专门为大规模数据集设计的引导程序相关的局限性。这将通过分析已知适用经典引导程序或其修改的各种场景来实现。如果可用方法失败，我计划开发继续适用的替代方法。随着数据集的增长速度不断加快，对量化统计程序不确定性的快速而准确的程序的需求很高。我的长期目标是使科学界能够对现代数据世界中越来越常见的新型大型杂乱数据集进行快速可靠的推理。上述研究将为深入、全面地研究此类程序提供第一步，并使研究人员和行业专业人士能够充分利用他们收集的数据。 该提案的第二个主要主题是联结函数在时间序列分析中的使用。自金融危机以来，众所周知，对经济变量或金融工具之间复杂的依赖关系进行正确建模极其重要。 Copula 提供了一种简单而优雅的方法来查找和验证此类模型。 在接下来的五年中，我的目标是扩展时间序列分析中的经典工具，以允许使用 copula 对时间序列动态中的分布效应进行可视化和分析。为此，我的目标是为统计界提供一个方法工具箱，这些方法以扎实的理论理解为基础，有详细的记录，并且对于非技术时间序列和联结界来说是可以理解的，并且在 R 中具有快速可靠的实现，以促进这些方法在广泛的应用研究人员社区和其他领域的广泛使用。