Robust and nonparametric methods for complex data objects

适用于复杂数据对象的稳健非参数方法

• 批准号: RGPIN-2019-04610
• 负责人: Chenouri, Shojaeddin
• 金额: $ 1.46万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765751
• 关键词: Robust; nonparametric; methods; complex; data

The research program proposed in this application is concerned with developing novel statistical and data science methods for the analysis of complex data arising in many areas of science, medicine, engineering, economics, and society. In most data analysis methods and all statistical modelling there are assumptions that are either implicitly or explicitly made. However, in practice and for real world datasets these assumptions are very unlikely to hold exactly. This is mainly because real world data are subject to error from many potentially unknown sources. So it is crucial to know how a method holds up if the underlying assumptions are violated, to what degree the method is resistant against these violations and how to develop methods that are resistant to these violations. This is the subject of robust and nonparametric statistics. When only one feature is measured from every subject under study (univariate data), the literature on robust and nonparametric methods is broad. On the other hand, when multiple features are measured (multivariate data), or one or more features are measured from every subject over time or space (functional data), the literature on robust and nonparametric methods is not well developed. This is even more crucial in the case of non-traditional datasets such as network and matrix valued data, where the literature on robust and nonparametric methods is almost of non-existant. The importance of robust and nonparametric methods is even more evident by noting that the quality verification of high-dimensional, functional, network, and matrix-valued datasets is an extremely difficult task and can not be done by manual or visual inspection. Therefore, there is a great need to develop statistical methodologies that are resistant to violations of assumptions, presence of outliers, and various model misspecification. In developing such robust and nonparametric methods, tools such as data depth, ranking or sorting of observations and various other procedures from robust statistics can play important roles. The objective of the proposed research program is to advance the current state-of-the-art in robust and nonparametric statistics by pioneering new tools or extending the existing methodology to more complex data structures. The emphasis is on performing theoretical studies and developing efficient computational algorithms. Some motivating application areas are neural spike trains, social networks, industrial process monitoring, additive manufacturing such as 3D printing, anomaly detection, environmental studies amongst other fields. In summary, the advancements achieved under the proposed research program is anticipated to have a significant impact on statistical data analysis and inference, and subsequently to science, technology and society through their application.

本申请中提出的研究计划涉及开发新的统计和数据科学方法，用于分析科学，医学，工程，经济和社会等许多领域的复杂数据。在大多数数据分析方法和所有统计建模中，都有隐含或明确的假设。然而，在实践中，对于真实的世界数据集，这些假设不太可能完全成立。这主要是因为真实的世界数据容易受到来自许多潜在未知来源的误差的影响。因此，关键是要知道如果违反了基本假设，该方法如何保持，该方法在多大程度上抵抗这些违反以及如何开发抵抗这些违反的方法。这是稳健和非参数统计的主题。 当每个研究对象只测量一个特征时（单变量数据），关于稳健和非参数方法的文献很广泛。另一方面，当测量多个特征（多变量数据），或测量一个或多个特征，从每个受试者在时间或空间（功能数据），文献的鲁棒性和非参数方法是没有得到很好的发展。这在非传统数据集（如网络和矩阵值数据）的情况下更为关键，其中关于鲁棒和非参数方法的文献几乎不存在。 鲁棒和非参数方法的重要性更加明显，因为高维、函数、网络和矩阵值数据集的质量验证是一项极其困难的任务，无法通过人工或目视检查来完成。因此，非常需要开发能够抵抗违反假设、异常值的存在和各种模型错误指定的统计方法。在制定这种稳健的非参数方法时，数据深度、观察结果的排序或分类以及稳健统计的各种其他程序等工具可以发挥重要作用。拟议的研究计划的目标是通过开拓新的工具或将现有的方法扩展到更复杂的数据结构，来推进当前最先进的稳健和非参数统计。重点是进行理论研究和开发有效的计算算法。一些激励应用领域包括神经尖峰序列、社交网络、工业过程监控、3D打印等增材制造、异常检测、环境研究等领域。总之，在拟议的研究计划下取得的进展预计将对统计数据分析和推断产生重大影响，并随后通过其应用对科学，技术和社会产生重大影响。