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: 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=685485
• 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.

本提案中描述的研究议程有两个主线：海量数据集的推理过程和时间序列分析中copula的使用。******随着现代数据收集技术的发展，超大数据集变得越来越普遍。为了从这些数据集中提取有用的信息，需要开发能够处理大量数据并在计算上仍然可行的统计程序。这激发了第一个研究方向：大规模数据集的快速引导过程。这部分研究的目标是深入而全面地理解专门为大规模数据集设计的bootstrap程序的局限性。这将通过分析一系列已知适用经典自举或其修改的场景来实现。在可用方法失败的情况下，我计划开发继续适用的替代方法。随着数据集的不断增长，对统计程序的不确定性进行量化的快速和准确的程序有很高的需求。我的长期目标是使科学界能够对现代数据世界中越来越普遍的大型和混乱的新型数据集进行快速可靠的推断。上述研究将为深入和全面研究这些程序提供第一步，并使研究人员和行业专业人员能够充分利用他们收集的数据。******本提案的第二个主题是在时间序列分析中使用copula。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依赖关系的正确建模是极其重要的。copula提供了一种简单而优雅的方法来查找和验证这些模型。***在接下来的五年里，我的目标是扩展时间序列分析的经典工具，通过使用copula来可视化和分析时间序列动力学中的分布效应。为此，我的目标是为统计社区提供一个方法工具箱，这些方法建立在坚实的理论理解基础上，对于非技术时间序列和copula社区来说，这些方法具有良好的文档和可理解性，并且在R中具有快速可靠的实现，以便于在广泛的应用研究人员社区中广泛使用这些方法。