Distributional effects and computational challenges in modern data analysis

该提案中描述的研究议程有两个主要线索：在大规模数据集中进行推理的程序和在时间序列分析中使用copula。随着现代数据收集技术的发展，超大型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保持计算可行性的统计程序。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了解与专为大规模数据集设计的自举程序相关的限制。这将通过分析广泛的场景来实现，其中已知经典引导或其修改是适用的。在现有方法失败的情况下，我计划开发继续适用的替代方法。随着数据集以不断增长的速度增长，对用于量化统计程序的不确定性的快速和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和混乱的数据集进行快速可靠的推理。上述研究将为深入和全面研究此类程序迈出第一步，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。该提案的第二个主要议题是Copula在时间序列分析中的使用。自金融危机以来，众所周知，正确建模经济变量或金融工具之间的复杂依赖关系是极其重要的。Copula提供了一种简单而优雅的方法来查找和验证此类模型。* 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，以便通过使用copula来可视化和分析时间序列动态中的分布效应。为此，我的目标是为统计界提供一个方法工具箱，这些方法基于坚实的理论理解，有充分的文档记录，并且可以为非技术时间序列和copula社区所理解，并且在R中快速可靠地实现，以促进在广泛的应用研究人员社区中广泛使用这些方法。

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.