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: 1404891
• 负责人: Xiaohui Chen
• 金额: $ 15.14万
• 依托单位: University of Illinois at Urbana-Champaign
• 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 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1404891&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受到了广泛的关注。该项目涉及高维多时间序列的各种估计和统计推断问题，这是时空统计，生物医学工程，环境科学，金融和信号处理中广泛的真实的应用中看到的一种普遍类型的数据。从大量的时间序列中提取信息是一个重要的研究课题，而时间序列的二阶结构在这些应用中起着基础性的作用，本课题的研究成果将为高维时间序列的时空协方差、精度矩阵及其相关泛函的估计和推断以及时变图的绘制提供理论基础。所有的问题都联系在一起，以描述具有非线性和非平稳时变特征的高维时间序列的二阶性质。我们还将研究增强的方法，占时间和空间的依赖结构。研究结果对于理解高维相依数据的动态特性具有重要意义。特别是，这些技术适用于生物医学工程问题，如通过使用功能磁共振成像数据建模大脑连接网络。

项目成果

Approximating high-dimensional infinite-order $U$-statistics: Statistical and computational guarantees

近似高维无限阶 $U$-统计：统计和计算保证

• DOI: 10.1214/19-ejs1643
• 发表时间: 2019
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Song, Yanglei;Chen, Xiaohui;Kato, Kengo
• 通讯作者: Kato, Kengo

Randomized incomplete $U$-statistics in high dimensions

• DOI: 10.1214/18-aos1773
• 发表时间: 2017-12
• 期刊: The Annals of Statistics
• 作者: Xiaohui Chen;Kengo Kato