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，对高维独立数据的分析引起了很大的关注。该项目涉及高维多个时间序列的各种估计和统计推断问题，这是一种在时空统计，生物医学工程，环境科学，金融和信号处理中广泛应用中看到的通用数据。作为一个重要的研究问题，应该从大量时间序列中提取信息，其中二阶结构在这些应用中起着基本作用。从该项目开发的结果将为估计和推理时空协方差和精度矩阵，其相关功能以及高维时间序列的时间变化图提供理论基础。将所有问题链接在一起，以表征具有非线性和非平稳时间依赖性特征的高维时间序列的二阶属性。我们还将研究占时间和空间依赖结构的增强方法。这项研究的结果对于理解高维相关数据的动态特征很有用。特别是，这些技术适用于生物医学工程问题，例如使用fMRI数据对大脑连接网络进行建模。