Collaborative Research: Second Order Inference for High-Dimensional Time Series and Its Applications

合作研究：高维时间序列的二阶推理及其应用

• 批准号: 1405410
• 负责人: Wei Biao Wu
• 金额: $ 29.9万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1405410&HistoricalAwards=false
• 关键词: Collaborative; Research; Second; Order; Inference

During the last decade, analysis of high-dimensional independent data has gained substantial attention. The project involves a variety of estimation and statistical inference problems for high-dimensional multiple time series, a universal type of data seen in a broad spectrum of real applications in spatio-temporal statistics, biomedical engineering, environmental science, finance, and signal processing. As an important research problem, one should extract information from a large number of time series, where the second order structure plays a fundamental role in those applications.Results developed from this project will provide the theoretical foundation for estimating and inference of the space-time covariance and precision matrix, their related functionals, and time-varying graphs of high-dimensional time series. All of the problems are linked together to characterize the second order properties of the high-dimensional time series with the non-linear and non-stationary time dependent features. We will also study enhanced methods that account for the temporal and spatial dependence structures. Results from this research are useful for understanding the dynamic features of high-dimensional dependent data. In particular, the techniques are applicable to biomedical engineering problems such as modeling brain connectivity networks by using fMRI data.

在过去的十年中，高维独立数据的分析引起了广泛的关注。该项目涉及高维多时间序列的各种估计和统计推断问题，高维多时间序列是时空统计、生物医学工程、环境科学、金融和信号处理等广泛实际应用中常见的数据类型。作为一个重要的研究问题，人们需要从大量的时间序列中提取信息，其中二阶结构在这些应用中起着基础性的作用。该项目的研究成果将为时空的估计和推断提供理论基础。协方差和精度矩阵、它们的相关泛函以及高维时间序列的时变图。所有问题都链接在一起，以表征具有非线性和非平稳时间相关特征的高维时间序列的二阶属性。我们还将研究解释时间和空间依赖性结构的增强方法。这项研究的结果有助于理解高维相关数据的动态特征。特别是，这些技术适用于生物医学工程问题，例如使用功能磁共振成像数据对大脑连接网络进行建模。